I have had HOMM3 up and running and have played it quite a bit since my initial purchase, however I have noticed an increasingly irritating bug that causes the game to crash whenever my screensaver kicks in. This is a relatively minor problem, as I am often saving to prevent loss of data.

I was just wondering if this has been a problem has been an issue for other players and if anyone has found a solution that is not along the lines of, "turn off your screensaver" or, "download third-party software to disable the screensaver when HOMM3 is running." It would be nice to be able to walk away from the game for a few minutes without having to worry about restarting when I come back.

Perhaps alt-tabbing out of the game when you leave it on prevents the crashing?

While the HD mod is absolutely a recommendation, it's not true 16-bit mode no longer exists. In fact, Windows 10 can run a specific executable in 16-bit colour mode if you set it as such in the Compatibility tab.