Why does my wow realmlist keep refreshing
Why does my wow realmlist keep refreshing
You might wanna try using the WoW repair program that comes with the game. This will scan through the folders that the game is in and see if anything got corrupted. If this does not work you can ask on the official WoW forums in the tech support section and they can try and help you.
If this happens on a Tuesday, then it could be that the realms are just down for maintenance.