Thanks for the update. It sounds like there is something consistent about the connection between your two machines that is losing data and causing the host and client game to get out of sync during a data transfer.
Are either of you running any other programs that are communicating over the net (voice chat, file transfer, etc)? If so, try playing with these running.
If you have a security or anti-virus program, or other software that might be watching all network traffic, I would suggest disabling it temporarily, as a test, and see if that effects the game connection.
Do you have another computer available, or can either of you try playing a different opponent, just for testing purposes? This could help narrow it down if the problem is related to one of your machines or one of your internet connects / ISPs.