I had the same problem for years, despite otherwise good health, and I took, on different occasions, Levaquin, a Z-pack, and Augmentin. Awesome antiobiotics indeed, they killed every pathogen in my body except several in my sinuses, which grew back immediately.
According to Mayo Clinic research, sinus infections don't follow the regular model of tissue infection. I've born out that research with a sinus flush that washes out the infected mucus, and I am on my 5th year of clear sinuses. If you have tried a regular saline irrigation, it won't work, because gravity prevents the saline from reaching the upper sinuses, where long-term infections often reside.
http://www.medhelp.org/user_journals/show/2322
The Flip-Turn Sinus Flush is mildly risky, because you have to bend over to do it, preferably in a shower, but you can also do it outside on soft ground.
In your case, due to your other problems, I'd recommend the Reverse Flush (Chapter 13). I'd also recommend going to the ENT, to see if there are any physical obstructions in your sinuses.