Jim, I had the same problem with my new AVR7300. At first, I thought I had a problem with the in-wall wiring to the surrounds. Turns out the wire was literally hanging by a thread on the suspended center channel speaker. I have since installed banana plugs on all speaker wires, both at the receiver and at the speakers.
My point is that you should check and re-check the speaker wiring, especially for possible shorts. Also you should be using no smaller than 16 gauge wire.
Disconnect all input and output cables and, with the "naked" receiver plugged into the wall, if the receiver will still only stay on for a few seconds, there is a problem. There could be a "auto on" function that you must click on/off to allow the receiver to stay on. Check your owner's manual and then give HK a call.