Generally speaking it sounds as if the apartment complex is trying to keep folks that do not live there from coming there, especially trying to keep folks who do not live there from coming there with firearms to shoot up a) the tenants, b) the complex structure, or c) both. This is what is known in the forensic business as "a clue" that there might have been incidents of a), b) or c) that happened there in the past.
It also means you will most likely be hassled or even evicted if you OC around the complex. But there does not seem to be anything that would forbid you from keeping a legally possesed firearm in your apartment, which also means you should be good to go regarding taking it out and bringing it back for such activities as repairs and recreational shooting done away from the apartment complex. You might want to check state laws about whether cased, unloaded firearms moved between your residence and your vehicle are considered concealed. If you plan to OC while away from the complex you should consider how you are going to handle getting from your apartment to your vehicle and back again so as to attract the least attention while remaining legal regarding concealed carry laws. Just don't make it any more complicated than it has to be, and try to figure out a way that does not involve removing your handgun from the holster (which is when you are more likely to have something go wrong that when it's securely in the holster).
Look especially at sections 1312 and 1342 of http://www.azsos.gov/public_services...esidential.pdf
to see what's what. I do not know what the AZ courts consider "unconscionable" but outright prohibiting of firearm possession might qualify.