My Linksys WRT610N seemed to be almost dead in peripherals.

I’ve decided, that I have nothing to loose and performed hard reset.

After router booted up, I have reconfigured it manually and everything worked perfectly: internet, even both Wi-Fi interfaces.

Had to dig internet a bit to recall on VPN configuration, but eventually VPN works also.

My guess is that during power loss occurrences the voltage from power supply felled too slowly and that lead to flash memory corruption where the settings are held.

Implicitly it is proved by the fact, I have switched electricity many times off and on just previous two days before failure.