We have a large team of User Account Administrators that use Terminal Servers to manage user mailboxes through Active Directory Users and Computers, and use the Exchange System Manager to manage mailboxes on the our Exchange Servers. I had to remove and reinstall the ADUC. I followed that by reinstalling the System Exchange Manager. Now it continues to attempt to install Exchange manager over and over. The Terminal server is running Window 2003 sp2. Does anyone know how to stop this behavior?

Not sure what you mean by resintalling over and over, but make sure that you also reapply any service packs and rollups to match the same level as the Exchange Server. Also make sure that no one else has it open when installing.