Stabilizers don't fix the problem the mask it. The more times it wobbles the worse the parts wear out including trashing your stabilizer. So all I can suggest is go through the whole front end. Check all parts, bushings, ball joints and tierods. Check all bolts and double check the track bar. Did you have the tires checked for balance.
08 Black and Khaki JK Sahara Unlimited, Dual Tops, MyGig, Tow pkg, Trax-Lok Rear Diff,
Mods -- 3.5" Rock Krawler front springs, 2.5 TerraFlex BB, PitBull Rockers 35x12.50x17 on BlackRock Vipers, AEV Premium Bumper,