Follow up from San Antonio News says they can evict him.
http://www.mysanantonio.com/news/local_news/Eviction_stands_for_man_who_shot_at_thieves.html
Eviction stands for man who shot at thieves
[...]
If the man doesn’t move out, Ray says the complex has to file an eviction lawsuit, which usually takes about two weeks. That gives the man at least a little more time to move.
Landera Apartment management declined to comment.
I'd love to see the contract that renters have to sign, to see how the gun ban is worded.