In the word “appetite” T is between 2 vowels and it’s not flapped T according to Oxford American English dictionary. Why?
The main reason for not flapping a T that is between vowels is how the vowels either side of it are pronounced. For example, a 'T' followed by a 'silent E' is not usually flapped, such as in late, ate, plate etc.
In the word appetite there are two Ts, and both are flanked by vowels, technically. But the second is followed by a 'silent e' which acts on the letter 'i', changing it into a long vowel. The letters 'ite' should therefore be considered a unit of speech, and that is why the preceding 't' is not flapped - the 'i' does not belong to that unit.
Even written rules of English commonly have exceptions, but you're referring to nothing more than a 'rule of thumb' for certain English dialects.
The first "t" in "appetite" is not flapped because flaps only occur in unstressed syllables. That syllable, "tite", has a secondary stress:
The 'ˌ' symbol before the /tīt/ indicates a secondary stress.