The problem:

A CVSNT user can commit some files but other files come back with a rather cryptic message saying permission denied:

The server reported an error while performing the "cvs commit" command.
version3: cvs server: cannot change mode of file /cvsrepos/test.cfm,v: Permission denied
version3: cvs [server aborted]: cannot rename file /cvsrepos/,test.cfm, to /cvsrepos/,test.cfm,: Permission denied

This is caused by the Windows account associated with the cvs user not having enough permissions to overwrite files saved by another Windows and cvs user.

The Solution:

Grant the Windows user associated with the cvs user more permissions in Windows.