Open Resources on Windows NT Server 4.0

Our network keeps slowing down and it seems to be caused by open resouces not being released at the server. Our Server is an Pentium II 450MHZ, 512MB Ram, 2-18GB Hard Drives (Mirroried), NT 4.0 SP6, 10/100 NIC and 10/100 Switch supporting about 60 users. When running a DOS based program and users exit the program, the NT server shows the resource is still open for that user even though the user does not have the program open. Until I manually release the resource does the program/server speed back up. Any Ideas?