What could cause my car stereo to sound great when key is switched on but cut out when engine running?

stereo sounds great when ignition is on and can play as loud as i want but when engine is running and i turn the music up to a reasonable level, it begins to cut out. memory wire is ran to "batt" on fuse box and power wire is wired to "ign" on fuse box. ohm meter shows steady 15 volts all the way from battery to the back of the head unit. i have tinkered with the ground several times with the same result. even exchanged head unit for another brand new one and have same issue. no wires are crossed or making contact with anything