It depends on what your lease says. <br />
AC isn't a necessity like heat or water - they may have every right to take their time fixing it, and maybe not have to do it at all.
Since you have already made several requests, and they are on paper. That's great on your part. Every parish has different rules. I would call the Justice of the Peace office in your area and ask them that question. I do know that it is the law that a landlord or apt complex cannot rent an apartment without 2 things. 1) a.c. 2) heat... An apartment would be declared inhabitable if so....
If you're paying for AC and not getting it I would tell them they're being dishonest, you've given them enough time, and you're going to call a lawyer if they don't get someone to fix the unit in that week.
You are paying for an air conditioned apartment, right? Everything is supposed to work, right? Call HUD and see what they say. This happened to me once and I told them that for everyday they didn't fix it, I was going to deduct $25.00 from my rent. I also threatened to call Child protective services because I had a child in a swealtering apartment and no air conditioning. Look in the phone book for anything that has to do with housing development. Or call a lawyer. They do have to fix it. Slum lording is against the law in most states. Good luck.