You have to understand electronics.
I'm not saying this is how the x36 is designed, but it's one possibility, and fully explains how firmware can control hardware. (or fail to control it)
If the clock battery charging circuit is controlled by the CPU, then the CPU (hence the firmware) controls when it is being charged and when it's not. If a malfunction causes a bit to get stuck in the wrong position, that signal may never be sent to charge the battery. Thus, the battery goes dead and the clock loses time.
Another theory I floated recently is that the display dimming and the clock might be related. If the same regulator is used for both, and if that regulator is failing, it could affect both the voltage the backlight receives as well as that the clock battery receives. Both are conditions that take time to develop, and it's certainly not beyond possibility that they are related. The regulator could also be controlled by firmware.
As I said above, the HP-x series does not seem to exhibit this issue, and they reportedly use the same hardware design.
Firmware doesn't have to have updates to be altered. It reads data off an SD card which I bet has been changed by you many times. Perhaps a corruption in the card set the aforementioned bit.
One more possibility: The firmware is supposed to charge the battery to capacity and stop. What happens if it doesn't stop? Like any battery that is continually charged, it will die a premature death. Note that these symptoms are identical to a "bad battery", and changing the battery will solve the symptom, BUT NOT the CAUSE. Perhaps this is what Uniden is looking into. Again, that's a firmware bug that imitates a hardware flaw.
There are a ton of causes that can make the issue a firmware issue, and it's pointless to guess exactly what the issue is. I only mention a few to prove it's not far fetched that firmware that controls hardware can fail to control hardware given the right (or wrong) circumstances.
One thing that is clear: The RTC failure seems to be caused by a voltage failure. What is causing the voltage failure? Is it a bad battery? A bad charging circuit? A cold solder joint? Or is it something that is in the firmware that is malfunctioning (a bug)?