stereo in 94 golf needs attitude adjustment

The power to my stereo kinda randomly flips off, then on, then off, and so on... It happens especially at night when the headlights are on. If i turn the stereo and headlights off, let it sit for a few seconds, then turn the stereo back on(w/ headlights still off), it works for maybe two minutes until the whole cycle repeats itself. Playin tunes at high volumes also consistently lead to the stereo's off/on problem. I prob shouldn't say it happens just at hight volumes or at night, cause it happens all the time, really. But those two factors def make the problem worse.
My guess was just a bad head unit, but i just installed a new aftermarket unit, and it does the same thing. Now i'm thinking a ground or relay problem, but who knows. Any ideas?!?

Thanks,
~C

if it was a grounding problem, you'd think the power would shut off randomly, not just with ac or high volume. Best shot would be the relays, unless ur alternator is weakening :/.