Eerrrr that sounds like something drastically bad happening. The HeaterMeter runs independently of the Pi so it should be rock solid despite any software weirdness happening on the Pi or something crashing there or losing network connectivity. If the HeaterMeter locks up to the point it stops at whatever output it was at and not show any probes attached on the display, something is horribly horribly wrong in hardware causing something to completely affect the microcontroller's physical operation. Or are you saying that just the webui wasn't working?
The servo losing its configuration is pretty odd too, because the only way it could reset to default is if the EEPROM became corrupted on the microcontroller and it had to reset itself to the defaults, which is everything on the configuration page. Although if the microcontroller is locking up for some reason, which would likely be power-spike related, it definitely could also reset the EEPROM as one of the symptoms.