Yup you have a bad soilder joint on the circuit board.
I have run my own electronic repair shop on the side and have been doing repair for about 11years.
If you like to ship the amp to me I will fix it for nothing. I have everything to trouble shoot audio circuits.
If you do want to do it yourself. Get a plastic stick or something small that doesn't conduct. Take the cover off and with power on tap around inside.
When you start getting close to the loose part (cap, transistor, resistor, IC, coil.) it will cut out and back on with the taping. With the way they wave soilder the pc boards these day bad soilder joints r very common in everything. After you get close mark the area with a marker, tare the rest down (mostlikely you will have to remove the transistors from the heatsink which is the casing) you will need heatsink compound (its that white stuff you see inside the amp, radioshack has it still I think) then use soilder iron to repair the connection.
If you take a pic of the board, I can break the sections down for you and give you some ideas where you might want to start looking. And watch those caps, they can store 50-100 volts even after you unplug the unit.
