Are they auto hubs? If so they could be broken or need a cleaning. Auto hubs disengage when you drive in reverse, which is why you don't hear the clicking noise. Next time you have both wheels on jackstands try turning the drive shaft coming out of the transfer case, when you do this you should be able to see the axle shaft turn until it locks the hubs. If you have a broken or dirty hub then you will see the axle shaft on that side continue to spin without engaging the wheel.
If you have a dirty hub then your job is easy, clean it with brake cleaner! Once you've cleaned your hub don't pack it with grease (which will prevent the hub from engaging properly). Instead, coat it with some ATF.
Here is a write up you can follow along in the tech library:
http://www.therangerstation.com/tech_library/HubDiagnosis.shtml
Your hub might be broken, but a good cleaning is worth a shot before spending money on new hubs. Sorry for your troubles, auto 4x4 sucks. I know, my truck has it!