Why is the second t in "aptitude" aspirated?

Solution 1:

For some speakers, voiceless plosives are not only aspirated at the start of a stressed syllable, but also at the start of an unstressed syllable. In American English, aptitude is pronounced something like /ˈæp.tə.tuːd/ (by contrast, it's /ˈæp.tə.t͡ʃuːd/ in British English); the t's are syllable-initial so they're aspirated for some speakers:

  • [ˈæp̚.tʰə.tʰuːd]

So it's no wonder you hear aspirated t at that position.