Its MOST likely a loose solder connection somewhere in the unit, maybe on the front panel jack, maybe on the volume pot. It could also be the output IC TDA2050, but usually when those blow they don't sit there humming away afterward, I would suggest looking thru the unit for problems like the ones listed here. http://tetsuoelectronics.wordpress.com/2011/06/04/fender-pro-jr-no-output/
To trace the problem better, take out the amp chassis as shown in the step by step, then with the back PLASTIC end of the screw driver, tap around and see if you get the sound to cut in and out on a specific part of the board, if so its probably your culprit. When I used to fix these a a lot I would just resolder the whole front and back panel as this just guarantees no more issues in the future. Let me know if this works, if not I can walk you thru a few other ideas. Thanks