Can a senior apartment deny my mom residence because she has Alzheimer's?

Much depends on how the apartment is funded. If it's a private facility, likely they can say that they aren't prepared to help people who have dementia. If the apartment is subsidized with Federal money, that may change the picture. You could with check your city housing authority to learn more.
Good luck,
Carol

The apartments I am referring to are subsidized by HUD and they cater to people with mobility limitations. It sounded perfect for them. When I went in to check their status, first a woman in the office told me that my parents were coming up soon...best news I've gotten from anyone..within 6 months! Then she looked at their app. and said it was flagged because my dad has a criminal record and gave me the case number! Then, I had a minor meltdown. turns out its a parking violation that was paid a long time ago! but in Palm beach they list those violations under "criminal" (unbelievable). Then, she said his debt was too high.. (he has excellent credit but did incur a lot of debt in the past 3 years trying to keep up) he is presently in the process of filing bankruptcy as he just cant carry the debt on ss and tiny pension. Then she said my moms condition could keep her out because she can't live independenty. Needless to say I got to sleep at 5AM after crying my eyes out....again.... thinking about all that bad news at once. Ugh! People. So totally incentitive and anxiety provoking in manner of handling others. In any case thank you for the advice. I will contact my city housing authority.