I had the same problem on our 2005 TJ that was still under warranty, just about a month ago. It was scary and dealer couldn't fix it. Turned out to be the stock shocks were fried. We never go off road, just California freeways but the stock shocks are really bad. The original tires, although only half worn were badly cupped from the bad shocks. I had to get new tires and shocks so I figured it was time to upgrade and went with 31" tires and a BB lift kit. Not happy with the cheap RE shocks so I'm waiting for OME Comfort shocks to come in.
2005 Solar Yellow X
Automatic/Soft Top/OME Shocks/RE 2" BB/31"x10.5" Tires