I have a 2005 jeep liberty, always runs great. But just the other day it started making a thumping noise, over 35 mph on the drivers side rear wheel. It comes and goes and doesnt always do it. I had the tires balanced and rotated, but that didn't fix the noise.
Raise that tire in the air that is suspect, and spin the wheel with your hand running over the tire slightly. You may have a belt that is bad in the tire. You should have a bulge in the tire. This will cause a thump while the tire is spinning. Sometime you can't see it, only feel it. Give that a shot.