I had this issue today, and what fixed it for me, and then later on other users whom I suggested it to was the following:
1. Close Demigod if it is open
2. Launch Impulse
3. Click the Community Tab in Impulse, then Click the Games Tab (at the bottom) within the Community area.
4. Create a game (top right)
What this will do is launch demigod, with you automatically logged in hosting a game. You can then cancel your created game and you'll still be logged in and your login issues should be fixed. I was able to login/off fine normally after that.
