Your phone probably has some sort of power keeping it alive, that or it has the kind of ram that can hold information while out of power.
Most modern-day phones don't actually keep time once the phone is turned off, it simply retrieves the time once it gets connection to a cell phone tower as part of the boot process.
the reason it needs power to store things like clock time is because it needs to constantly update the time
if it didnt need to then it could store it in ssd-like flash storage
however im not sure if there's something actually preventing an upgrade from volatile memory to non-volatile
Theoretically you could have the BIOS settings stored in non-volatile storage, but the battery would still be required to keep the clock ticking if the power supply is shut off or gets no power.
I was told that the CMOS clock maintains the system date and BIOS settings. Should the battery stop holding power, the date gets reset and the checksum goes bad. The time is getting reset on this PC every time it is unplugged.
Definitely a dead battery then.