so basically u got a short somewhere, it was working fine when they were both hooked up to the ignition 12v right?(besides memory loss, it wasnt flickering or anything) so it more than likely ur constant 12v is shorting out, try to trace the wire far back as possible or see if the fuse is loose. If ur to lazy to do that shyt just run a wire from a constant 12v source then hook it up and see what happens. Or another reason why it might be doing that is cause ur radio is shytty.