Brian Collins’ answer is impeccably correct for why pronunciation was not spelled pronounciation after the combination of the Great English Vowel Shift and Trisyllabic laxing (a long vowel three syllables back is shortened, as in insane ~ insanity). But all the answers aren’t really answering why pronunciation is still being pronounced pronunciation.
Let’s look at another instance of trisyllabic laxing: private ~ privacy.
In Britain, privacy has a short vowel, following the same rule as insanity and pronunciation. In the US and Australia, it’s a long vowel.
Is that because the US and Australia are illiterate? Why then, so are the British, when they say pirate ~ piracy, with a long vowel. (I’m told piracy still has a short vowel among laywers.)
No, it’s because trisyllabic laxing has resulted in a lack of morphological transparency. The change in vowel looks wrong: if privacy comes from private, they should sound the same. And they’ve been made to sound the same again, a few centuries later, by analogy.
Well, just as piracy has come to sound more like pirate by analogy, and privacy has come to sound more like private, now it’s pronunciation‘s turn. People are tempted to pronounce it pronounciation, for the same reason. I do. And it’s not currently considered correct, but it may yet.