Different by manufacturer. Some (Oticon Bernafon) program on the fly, so as long as it didn’t happen the instant a change was happening, you’d be ok based on the previous write to the EEPROM. Sonova product requires a session end re-write and re-boot which is a bit more fragile, especially if the failure occurs during the write window.
In either case the option to revert to previous session data, or potentially the current session data in the software that failed to upload during your outage is usually available. Even if it has to follow a ‘factory reset’ of the aids.
I’d guess that there was probably a bigger risk during firmware updates: when they shut down during a full reprogramming, there’s obviously reasonable potential to corrupt an aid. Especially as it takes a reasonably long window to complete a full rewrite of the hearing aids.