Yes, if you loose power, you also loose combustion air, the flames go out pretty quick. We have lost power a few times and the stove has restarted when still hot. BUT, it has made a real mess if it didn't. Once the power comes back on, the stove will keep stoking to satisfy the thermostat, and if it flames out, it just keeps pushing coal!!! with no flame
I am putting a low temp switch on the flue pipe (<100 deg.) and it will kick out the stoker unit if the temp drops below that (flame out condition), but if it does relight, the switch will kick in and everything operates correctly.
You could put a battery backup on it if needed to keep it running for a short period of time (30min-couple hours).