When my opponent disconnected without playing a move, I had no way to escape from the game. His clock kept ticking down. I logged off and logged back on. The game was still there and when I clicked on it I was charged with a resignation. I never clicked resign. There needs to be a way for an abandoned game to be ended.

Did you try waiting 10 minutes? On the old site, I don't know if it's true here as well, a player who is idle for 10 minutes forfeits the game.
 
But either way, it shouldn't charge you with a resignation when you try to return to the game. That looks like a bug.

Yes we will implement a procedure for handling a disconnection in a live game with a longer time control. It is still under review. I believe on the old site if your opponent disconnects, you can wait a few minutes for them to return, if they do not you can choose to abort (cancel in effect), or you can wait the full 10 minutes and then claim the forfeit.
 
Please post any suggestions you have for handling this situation.

The way a disconnection is handled on Classic Caissa is just fine and it should be the same on New Caissa.