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

I hope this thread isn't completely dead yet... The other day, a friend and I installed Hamachi (version 1.0.3.0) to play Heroes 3 (the version with the Platinum Edition and the unofficial patch, and we both have it). We disabled our antivirus programs, firewalls, and everything else... We created a server, connected, and started playing. And then a problem arose: during the game, either I or my friend would get disconnected. Most often, this happens when someone takes their turn. A message appears saying that one of the players has left the game (if that player was the server, another player becomes the server). The game doesn't end, it just replaces the friend with a computer AI. The most interesting thing is that, for my friend, the opposite happens – it says that I'm the one who left. This is a very strange issue. Does anyone know what this is related to? And how can we fix it? We just want to be able to play normally.