Disassemble the trap, check the mating surfaces of the 90 for imperfections. Coat those surfaces and the trap threads with a then layer of teflon non hardening pipe dope. Reassemble the trap by tightening the 90 first then the flex part. The dope will fill any voids on the mating surfaces and help lube the threads for a little extra turn while tightening.
I think I might have finally figured it out. I put a rubber gasket around the tapered end of the 90, and tightened it to the trap. So far it hasn't leaked in 8 hours. Ran some water through it again this morning, and still didn't notice anything.