I've played a few matches with my friend in 0.1.5 that all ended in connection issues. While I do see that a solution for that was added recently, it did give me an idea: Would it be at all possible to allow unfinished matches with another person to be continued from saved replay data? Because the game is turn-based, that gives it a unique opportunity to allow both players to stop a match and come back to it later, like with a chess game, and I think it'd be a shame to not take advantage of that. I know replays already work this way in singleplayer, but I'd love to be able to continue from replays against a friend too. Maybe it could be exclusively for private matches, since I could imagine it being used to troll people by putting them in a losing battle.
My other suggestion would be to allow control over the HP, for short matches or if you wanted to do some long epic fight, which would go well with the ability to save a fight with a friend and continue it later.