How to play Heroes of Might and Magic III online via Hamachi?

Basically, I'm having this problem – maybe someone can help. I installed Hamachi, and for about a month, everything worked more or less fine. Now, I'm experiencing consistent issues. Here's the situation: if I create the game, others can see it, but when I try to send information, it fails. If someone else creates the game, I can usually join by using the IP address. The game starts, but when it's my turn to make a move, it fails about 30-40% of the time. I have to send the autosave to my opponent, and they load it, and then everything works fine. So, as I understand it, the problem is that data isn't being transmitted properly from my end, and it only happens in the game. For example, when using ICQ, torrents, etc., the outgoing channel works perfectly. The firewall is disabled, and I don't have any antivirus or firewall software installed. I suspect it's Hamachi, although I've tried many different versions (currently the latest one from their server), but nothing helps. Can anyone offer some advice?