It does sound like the symptoms my radio was showing. I opened the case, but I decided not to remove the printed circuit board to begin hunting for the problem's source. So I took the easy way out and sent it to Uniden repair. They estimate they'll ship it to me by Nov. 5, but repair status indicates they haven't actually started working on it yet. Your complaint's similarity to mine makes me think it's a common enough problem that they'll be able to correct it quickly. Estimated repair cost and shipping back to me total about $89 so I included a check. If more parts than normal are needed, they'll let me know. If it only needs a circuit component or a solder joint correction, I don't imagine I'll get a partial refund, but who knows?
In my case, I was forced to manually "avoid" all channels that stopped scanning, which left me with just one P25 system to monitor. Of course, if the scanner was stopped on a static-y conventional channel and there was activity on that channel, I could hear it just fine, but that's not a workable situation.
If I find out anything useful from Uniden's repair, I'll update this thread.