Some headunits are power hungry. I wired a (freebie!) JVC into my Stealth, and whenever I turned the volume over 20% it would keep cutting off, back on, off again, etc. until I turned it back down. It turns out the factory wiring was too small to keep up with the power demands of the head unit.

Recheck the wiring and fuses, then put a multimeter to the power and ground to make sure you are actually getting power and ground. After that, try running larger (stranded copper) power and ground wires.