There are probably several factors at play here. We'll need to discount accents like Cockney where h is generally not sounded anyway.
(1) In general, an h at the beginning of an unstressed syllable is silent in most accents of English: annihilate, vehicle. (I think some Irish accents might sound the /h/.)
(2) However, if this is an initial syllable (say hydrate), the rule is disregarded.
(3) There are style guides that indicate that an should be used before h if it occurs in an unstressed syllable, which results in some newspapers recommending writing an historic moment, for example, and a perception that this is the 'correct' way to write the phrase.
It seems to me that it is possible that as a result of (3), people are not pronouncing the /h/, because it is difficult to pronounce the /h/ after an /n/. It also seems to me that in speech, the 'an' joins up to 'historic', giving the impression of a trisyllabic word, and if you apply (1) above, the h should be silent.