I experienced this issue early on, and it's feedback of some sort. I've tried quite a few different power amps and some do it, some do not, also depends on the gain level setting. With my current Modwright KWH 225i I am able to leave them on all the time, with the gain ~8/10. On the other hand, my Cherry Golden mono-blocks go into "sleep mode" on their own, after a few minutes of silence, and I discovered that transition would set the bass amps oscillating each time. It's very annoying and there is no way to disable the sleep feature on those amps without sending them back to have it completely removed (also is a substantial cost).
So, Clayton's message is clear, just follow the turn on and turn off procedure and you'll be fine.