The creation of English dictionaries in the 18th and 19th centuries generally normalized and stabilized spelling for words in the spoken language. Lexicographers used etymology to inform the rules they applied. The point here is that pronunciation and spelling have a relationship that is more correlation than causation.
Others have mentioned prosody as a reason why we pronounce "cynic" and "cycle" differently. I suspect that the words in English also continue to reflect distinctions in the original Greek words κυνικός (cynic) and κύκλος (cycle). There are (at least) two import differences: (1) the first syllable is stressed in one and not the other and (2) the "consonant" after the vowel in question is voiced in cynic but not cycle (both in Greek and in English).
English vowel sounds change dramatically depending on whether the following consonant sound is voiced or voiceless. This is most apparent in short pairs like "bad" vs. "bat" where we pronounce the vowel before the voiced d much longer than before the voiceless t. In IPA, we write these sounds as [æː] and [æ], respectively.
So my answer (or guess, really) is that English patterns for differentiating vowels based on following consonants caused the preservation of distinctions in the original Greek.