DrAzzy:
I thought the bootloader was smart enough to turn off the WDT if it was started from a WDT reset, and not end up in a state where the WDT reset prevents the bootloader from running, though...
They're still using the crappy ATmegaBOOT_168_atmega328 bootloader for Pro Mini instead of optiboot which doesn't do this. ProMini: Reboot loop when using watchdog · Issue #150 · arduino/ArduinoCore-avr · GitHub. If it's an ATmega328P Pro Mini then you should be able to use it as an Uno and Burn Bootloader to fix the problem.