GOG version of the game is unbeatable, I can confirm the tread on GOG forum is true. The only legit way of playing without this nasty bug and actually finishing the game is to find the version that is not pre-cracked (unlike the GOG one) and apply the password for the game every time it is launched by using the password manager thingy that comes with the retail version or it's screenshot, and then calculate the right password for each sport in the game. Same applies to the Summer Challenge game.
https://www.gog.com/forum/summer_winter_olympic_challenge/old_drm_in_the_gog_version