Auto battle works, there's just a bug going around that glitches out the game and stops it from working. If you try to click the bottom left refresh icon, it gives you the bug where you can't do anything and blanks out your eidolon list forcing you to do a browser refresh. You can either resfresh the browser when this happens or just manually click battle every turn til the battle ends if you don't want to refresh.
I've only gotten it about 3 times in about 50+ runs.