Was the secret generated from a card that transforms in your hand?
This is a known bug. The only “fix” for now is to quickly force-quit (Alt-F4), then restart the game and hope it reconnects in time.
Since the bug is client side, your opponent may not have been affected, or may have already known this and done exactly that. In which case they were able to win because you were still waiting.
After 10 minutes the game is now over anyway; I assume that when both people disconnect and fail to return the game eventually ends in a draw (or is won by whoever dies first to fatigue as the game keeps drawing cards and passing).