I had issues with a slumlord in the Fort when I was a student (not same apartment complex as you but similar situation). They took forever to repair my AC in the middle of summer and my apartment was over 85 degrees and roaches began to come into the apartment.

I ended up reporting them to the City of Knoxville's Code Enforcement office. You can call them and arrange for them to send somebody to inspect the apartment.

http://www.cityofknoxville.org/publicservice/codes/

They will then make findings and send them to your landlord with 30, 60 or 120 days to fix.

Here's something I would've done if it was me. I would let them know about the leak one more time and tell them that they are breaching their lease obligations by not keeping the apartment in a livable condition. If that does not work, I would tell them you are going to report them to the City and have a Codes Enforcement officer inspect the property. This will hopefully scare them into taking action to repair the ceiling. The investigator will not only chekc out the ceiling but the ENTIRE apartment. My investigator came to look at the roach problem and a small hole in a window, and he ended up discovering that there was a ceiling air vent that violated fire codes. My landlord ended up with 7+ pages of violations to repair in 4 months. Needless to say, I moved out shortly after reporting them to avoid friction and they sold the building shortly thereafter.

Odds are, your complex is hiding violations. They will not want a code enforcement agent poking around their property. Use this as leverage and demand that they fix it.

This is in no way legal advice. Just something I would do in your situation.

Let me know how it goes. Good luck!