The "t" in "relative" can be voiced and flapped/tapped in American English. You can see it transcribed as /ˈrɛlət̮ɪv/ on oxfordlearnersdictionaries.com, and the OED gives the transcription /ˈrɛlədɪv/.
"Stress" is a word that different people use in different ways. To me, it seems clear that an English word pronounced in isolation will have exactly one syllable with the "primary stress" (although Araucaria suggests in the comments that even this is debatable).
But beyond that, there are different approaches to the terminology used to describe stress, accent, vowel reduction and consonant lenition.
What is "stress" phonetically?
I want to briefly discuss the phonetic correlates of stress since some of the comments have brought up differences in how different people "hear" stress in words.
Mattys 2002 reports the results of an acoustic study of words starting either with a primary-stressed syllable followed by an unstressed syllable (such as "prosecutor" and "presidency") or a secondary-stressed syllable followed by an unstressed syllable (such as "prosecution" and "presidential"). It was found that
the first syllable of initial-primary words (e.g., /'p̲r̲ɑ̲sɪ/ is higher pitched and longer than the second syllable in the same word (e.g., /'prɑs̲i̲). This contrast is virtually absent between the first and the second syllables of initial-secondary words (e.g., /"prɑsɪ/). With regard to amplitude, first syllables are louder than second syllables regardless of the stress pattern of the word. (pp. 258-259)
From this, it sounds like primary stress can in general be identified by the higher pitch (F0) and greater length (duration) of the syllable as well as the higher volume (amplitude) relative to the surrounding syllables. But syllables with secondary stress don't necessarily stand out in terms of pitch and duration from unstressed syllables.
Based on this, it seems likely that it is easier to hear the difference between primary stress and secondary stress than it is to hear the difference between a syllable with secondary stress and an unstressed syllable.
Araucaria's comments on my answer reminded me that it may actually not be correct to say that pitch is directly associated with primary stress per se. Rather, one viewpoint seems to be that high pitch is a realization in English of accent, which we can consider to be related to but distinct from stress.
A syllable with primary stress may receive pitch accent, but doesn't necessarily. This is my understanding after skimming "Sentential Prominence in English" by Carlos Gussenhoven.
Although Gussenhoven distinguishes between the concept of pitch accent and the concept of stress, he does treat "primary stress" as a valid concept that is used in his formulation of accentuation rules. He says
every word is assumed to have primary stress, stress level “1,” on the syllable with main word stress (2780)
Accentuation is in part morphologically determined: SALamander has an unaccentable stressed syllable in penultimate position (2802)
My impression is that we can empirically define "primary stress" as falling on the last accentable syllable of a word.
What is "secondary stress" and where does it occur in English?
According to Balogné Bérces Katalin's "The Pronunciation of English", the term "secondary stress" is correctly applied only to stressed syllables that occur before the primary-stressed syllable (p. 113). This definition seems to be related to a theoretical idea that all English words are stressed on the rightmost major stress ("prominence of the right edge") (p. 113). It's not clear to me if there is actually any way to differentiate syllables with secondary stress from syllables with unreduced vowels and some lower level of stress using phonetic as opposed to phonological criteria.
There are very few or no English words that start with two fully unstressed syllables (a blog post on John Wells's phonetic blog, "GIGO", identifies only "peradventure" and "forasmuch" as possible exceptions to this generalization) so in long words with the primary stress on the third syllable or later, there is generally a secondary stress on either the first or second syllable. Often secondary stress corresponds to a primary stress in a related, shorter word (p. 114). A word can have more than one syllable with secondary stress (p. 110).
Alternative definitions of secondary stress
Some sources do seem to recognize the presence of secondary stress on syllables after the primary stressed syllable, but I haven't been able to find a good description of how this alternative terminological system works. Wells has another blog post "irritating hamburgers" where he writes:
native speakers tend to perceive the penultimate syllable [of "irritating"], teɪt, as being more strongly ‘stressed’ than the final syllable ɪŋ. But what they want to call ‘stress’ is arguably no more than a way of saying that the vowel is one of the strong ones. Actual rhythmic beats following the main word stress accent are all pretty optional, which is why the British tradition is not to show any secondary stress in words like this: ˈɪrɪteɪtɪŋ, not *ˈɪrɪˌteɪtɪŋ. The alternative tradition, usually followed in the States and (for example) Japan, is to recognize a secondary stress on the penultimate, írritàting.
I don't know if there is any theoretical relevance to using the term "secondary stress" to refer to syllables like this as opposed to the term Wells uses, "strong vowel", or the term Balogné Bérces uses, "tertiary stress" (discussed below).
In any case, a syllable with this kind of "secondary stress" that comes after the syllable with primary stress cannot be accented in American English, so the contrast presented by Araucaria's answer between "abso-'lutely fan-'tastic" and "'famous 'rela-'tive (stress on -tive, badly formed)" is not relevant. The word absolutely can be accented on the third syllable in American English, but when that occurs, that syllable has primary, not secondary stress.
"Tertiary stress" (some people may have this on the last syllable of "relative")
The absence of vowel reduction in syllables in other contexts than the ones mentioned above is sometimes taken to be a sign of some third kind of stress (not primary or secondary stress). Balogné Bérces
call it "tertiary stress", and says that it can alternatively be called "minor stress" (p. 111).
John Wells has a blog post that presents a different terminological system where such syllables are called unstressed syllables with "strong" vowels, as opposed to unstressed syllables with "weak" vowels. He says that a stressed syllable can only have a strong vowel, but not vice versa:
Some analysts (particularly Americans) argue in the other direction, claiming that the presence of a strong vowel is sufficient evidence that the syllable in question is stressed. In the British tradition we regard them as unstressed.
("strong and weak")
Wells says in this post that the American English t-flapping rule generally only operates when the following vowel is weak. However, the Bert Vaux paper that KarlG's answer links to indicates that it is pretty complicated and difficult to formulate a complete description of when t-voicing/flapping/tapping occurs in American English, so it seems possible that Wells's analysis has some issues.
In Wells's analysis, ɪ in unstressed syllables can be strong or weak, but it can be hard to figure out which one it is. Wells uses the presence of t-flapping in "emphatic" as evidence that this word has a weak vowel in the final syllable.
The variability between the pronunciation of "relative" with lenited, voiced, "flapped" or "tapped" t and the pronunciation with voiceless, less lenis t could be explained as a consequence of speakers varying between using "strong" ɪ and "weak" ɪ in the last syllable (or in Balogné Bérces's phraseology, varying between having tertiary stress and zero stess on the last syllable). How to explain that variation (which as Araucaria points out may exist between utterances made by the same speaker at different times, as well as between utterances made by different speakers) I don't know.
By Well's account, the use of a strong or weak vowel in a word is not necessarily fixed, but can vary depending on the circumstances. For example, reduced pronunciations of function words have weak vowels, while emphatic pronunciations have strong vowels. I think the variation of /oʊ/ and /ə/ in words like "progression" would fall under the same rubric.
t-voicing seems mandatory in the words I've thought about where the stressed syllable comes immediately before -tive: native, dative, stative, assertive, abortive. This corresponds with what Alice Turk says in the paper that Araucaria's answer links to. (I'm not sure that all of the rules in that paper are accurate for my accent: the statement that "Word-initial alveolars are never flapped" seems questionable to me. I think I can voice and tap/flap the initial consonant in "to" (e.g. in "go to the store") and Greg Lee posted an answer saying he can flap the "d" in "I don't know" and the "t" in "I'll go tomorrow/today".)
When the syllable preceding -tive is has a reduced vowel, voicing seems to be more optional. However, saying these words to myself, I still seem to often used voicing in relative, secretive (as in "secret"), positive, definitive, dispositive, competitive, repetitive, inquisitive, prohibitive.
For some reason, I think I might feel less strongly inclined to voice the "t" in excitative, imaginative than in the words in the preceding list. But the pronunciations with voicing don't feel at all impossible, and may well be more common for me than the pronunciations without voicing.
For all words of this type, not voicing the "t" feels like something that I might do more often in slow speech.
Sources not linked in-line