If you both have verified your gamefiles (right click Medieval Dynasty in the list of games in your Steam library, pick 'installed files' and then 'verify integrity of game files' and afterwards restart your PC) and that doesn't help, then it's most likely a problem with the internet connection or the pc not being able to handle it.

You could try if switching host makes a difference (the current host can give the savegame to the other person so they can host the next time).