If your amp has effects in and out jacks, connect them with an instrument cord and see if the problem goes away. If it does, then get inside the amp and clean the effects-return jack's NC (normally-closed) contact pair. (They look like two small flat fingers pinched together; inserting a plug causes the contacts to separate.) If the jack is an enclosed type, good luck getting to the contacts.
You'd need to shoot some plastic-friendly spray contact cleaner inside the jack.
Caig makes some. Do NOT use this stuff on switches/pots unless you follow it with a lube after it dries, because it appears not to contain any lubricant.
If the problem isn't in the effects loop return jack, then you probably have a cold/broken solder joint somewhere OR a broken circuit board trace. These are generally not that difficult for a tech to chase down. If you want to chase it down yourself AND you know how to solder, all it really takes is something long and insulated (chopstick, for example) to press down on various points to trigger the problem. You'll also need a magnifying glass because trace breaks and broken solder joints can be really tough to spot with the naked eye.
