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!
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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
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