I would first suspect the foot switch jack assuming you are not using the footswitch. There are many components but switch contacts, especially on the jack are very suspect.
It will take a little patience to find the problem... vibration can rattle the contacts or any loose soldering.
Answers & Comments
The circuitry for the channel switching is rather messy; Here is schematic:
http://elektrotanya.com/fender_hot-rod-deluxe_sch.pdf/download.html
I would first suspect the foot switch jack assuming you are not using the footswitch. There are many components but switch contacts, especially on the jack are very suspect.
It will take a little patience to find the problem... vibration can rattle the contacts or any loose soldering.