Zach,
First impressions suggests that this is an issue with the FTP server running on your printer (which is a novel idea – something I’ve never come across before!).
One way to determine whether the problem is with BizTalk or your printer’s FTP server is to create another send port that FTP’s the message going to the printer to a different FTP server (say the in-build IIS FTP server). Alternatively, write a simple C# app to hit your printer’s FTP server with several connections at the same time and see what happens.
Let me know how you get on.
Rgds, Nick.