Diagnosis
The router's internal memory that holds your custom settings got corrupted when the power cut out unexpectedly. It partially reset, reverting some settings (like guest networks) to default while keeping others.
How to Fix It
You need to do a full, clean reset and restore from a backup if you have one. Unplug the router. Hold down the reset button on the back with a paperclip. While holding it, plug the power back in. Keep holding for about 10-15 seconds until the power LED starts blinking, then let go. This performs a factory reset. After it boots up (with default settings), log in and set up your main Wi-Fi. For guest networks, you'll have to recreate them and their passwords.
If That Didn't Work
If the settings continue to seem unstable or random after a full reset, there's a small chance the flash memory where settings are stored is physically damaged. The next step would be to update to the latest firmware immediately after the reset, before changing any other settings.
Heads Up
For the future, after you get everything set up perfectly, go to Administration -> Restore/Save/Upload Setting and save a backup configuration file to your computer. Also, plug the router into a surge protector or UPS battery backup to prevent this from happening again.