Had TONS of trouble with this since the game came out, none during beta.  Just put up with it and occasionally I could finish maybe 1/4 or 5 games.  Saw a post made by somebody else here with this solution, but it seems to have been deleted or something.

Anyways, this is in no way acceptable for a user to have to do, but I believe this was the solution.

"ImpulseOverlay.dll" in your bin folder of Demigod, rename to "ImpulseOverlay.org".

This fixed every problem I had with getting disconnected in games and bots coming in for players.  I can not see the connection status log however.  This is why this solution is unacceptable for a player to have to do.  Please, if this works for other players, stick this thread.  Nobody should have to go through playing a game for 30 minutes, have a random ping spike and get disconnected to have bots left over.  It sucks.