After being educated regarding VMWare's impact on the OS (not a factor with respect to the behavior we have been experiencing), I searched for different means to disconnecting the RDP session. It appears, from my initial testing, that the Terminal Services Connection utility, tscon.exe, provides a solution to the problem. From others' recommendations we crafted a batch file that will close the RDP session and then take the machine's logged on user to the console.
@%windir%\\System32\tscon.exe 0 /dest:console
@%windir%\\System32\tscon.exe 1 /dest:console
@%windir%\\System32\tscon.exe 2 /dest:console
This accommodates the User ID being 0, 1, or 2. Run this, click OK to dismiss the warning that your RDP session is closing, and the console is open for business. A new email request gets processed, as the console is not locked.