Will psychotropic medications, if used for many years, increase the incidence of senility or Alzheimer's?

Typicallly no, Dimentia and/or Alzheimers are genetic disorders. There are studies being conducted, but currently they are inconclusive, while it may possible, it all may also depend on the particular medicine in question.

I agree with J_9 - I've just finished modules on biochemical pharmacology and neuropharmacology so I'm not an expert like her but I do know something.

My understanding is Alzheimer's is predominantly genetic but with multiple environmental factors, also it hasn't been fully characterised as of yet. Therefore it could be possible but as far as I know it isn't a major line of enquiry (I did a quick check of Pubmed to look for recent journal entries).
I also agree that the medicine in question would be valuable to know psychotropic drugs are a pretty big category.