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

Who can help? We tried playing 1v1 through Hamachi. At first, there were problems with the Hamachi driver on Windows 7. We figured it out. We downloaded a different version of Hamachi. Everything was fine. We set up the network (or so we thought). We tried creating a game. Everything was fine. We played. After 4 days, the connection dropped. I exited the game for him. He exited the game for me. And it happens on different days. Is the problem with Hamachi or with Beltelecom? Maybe there's another way to play over the internet? Are there any knowledgeable people here? I would be very grateful!