No I haven't see this before, but you might try asking in your generation of vehicle forum instead of the Tuning & Customizing forum since this is a stock issue, not a modification issue.
I don't understand why you would not have demanded that they fix this problem when it was new under warranty. Even if they claim a warranty doesn't apply, it still had to work right at the point of purchase.
Anyway, that looks like a bug in the firmware of the Stereo itself, or some factory defect that only an engineer of the stereo could pinpoint. Does it have any method of data input that would make upgrading the firmware possible? For example an SD card slot or USB port? I suppose there could be a service port on the rear, but otherwise if there is no way to input data, there is no way to upgrade firmware if one even exists available to the public.
The only other thought I have is that in rare cases a device can get into a bad logic loop that requires a power cycle to clear, but I would have thought that between purchase and now, that you've had the battery disconnected at least once (to change in a new battery if nothing else) so whether a power cycle clears it or not, the problem is still present.
If I were you, I'd call around to local junkyards and see if they have any stereo pulls that match yours or at least are something you can live with, that match the wiring harness and steering wheel controls assuming you have those.
You can pull the original stereo at the junk yard and try the new one, having an agreement with the yard that you are not buying it "as is" out the door without trying it, rather only if it works while you're on their property trying it out.
You might mention what model of stereo you have. I did find a youtube video that shows how to access a hidden menu on (at least) one model:
If you don't care about steering wheel controls, then you can replace it with anything you want.