Hmmm, not sure what disconnecting/reconnecting the coach battery power would do unless there is maybe a thermal fuse in awning motor or power feed line (like a motor overload). Turn off the power and the thermal fuse cools and resets itself? If that does not work now maybe the thermal fuse has permanently opened......if in the motor; likely means a new motor perhaps?
If the awning has a control relay mounted in wall near the switch at the door......that may be the click sound you hear (I think that is what Cavie is getting at), or maybe it’s just the switch clicking?
I would also look for any blown fuses (marked awning) in your coach converter/inverter fuse panel......not familiar with your coach, so not sure where that is. You may have to do some voltmeter trouble shooting to determine where 12vdc is good and where it fails, if you can open up the switch plate without damaging the wall etc. The problem could even simply be a broken motor power wire inside the cable that exits the coach wall and runs along the awning arm to the motor.
Thor may also be able to advise you on where the awning fuse(s) and associated relay(s) may be located and provide a typical schematic. As PaulWadley advised earlier you may need to contact Carefree for tech assistance with your specific awning type so they can help you trouble shoot. They may provide a recommended wiring schematic too (although Thor may not have followed the vendor requirements).
Carefree Dealers