Krell makes a "Krell Link" that you can use for delayed startup. I use it on my system so the pre-amp starts first, them the amp. These amps draw a lot of current when they first fire up. It may be not getting enough juice at startup and shuts itself off. Perhaps try starting the one amp by itself and see if it stays on. If not, could be the amp of course. If you feel you need service there is a fellow that used to work at Krell that has a repair facility. I believe it is The Service Center, owner Steve Lacrone (spelling?).Google it. He is very helpful.
-John