A short should pop a fuse, somewhere, instantly. It sounds like an
intermittent open in the 12v line, or a bad common ground at the
outlet.

Sounds like the helm outlet is a connection point, a poor one at that,
to feed the stereo. Unscrew the centre insert or behind the panel
barrel and that should release it all for servicing or replacement.
Turn off the circuit and disconnect the terminals behind the (cigarette
lighter?) outlet, first, or disconnect the batteries.

The connectors on these things are usually push on spade connectors
which do not take to tightening well. The wire end terminals probably
are old and need new ones crimped on. Buy a decent crimper and keep it
aboard, if that is the problem, you might have more of the same
pending. It could be the wires are just twisted together back there,
I've seen worse.

Terry K