95 Odyssey radio on/off intermittent

Over the last few weeks we've noticed the Alpine after-mkt radio/CD
player quits and comes back on intermittently. It does not correlate
with bumps in the road since it happens sometimes at a traffic stop.
And now the radio pretty much just stays off (easily 90 percent of the
time), rarely comes back on. It has a momentary "Power" push-button;
in other words, not a mechanical clicking push-button that would enable
it to just come back on when outside power is restored (e.g., if the
battery was disconnected while the radio is on, it wouldn't just go
back on as soon as you reconnect the battery). I did check the fuse,
and it looks fine, and the one or two other things on the same circuit
work, and if it WAS a blown fuse, it wouldn't come back on at all. Any
thoughts? Thanks in advance!

 

Being aftermarket, I am concerned about the quality of the connections. The
only radio I had installed by the place that sold it (the price was right!)
was connected by twisting and taping the wires. Maybe that is what is going
on with the power wire.

Mike