We have found when using ThinPrint that eventually the local PRINTERS folder gets full of old receipt print jobs. When this happens the PC will stop allowing RDP to launch; sometimes it will start but never log in. This was true when we ran our own server and is still true with your setup.
To check if this is the culprit I view the Properties on C:\Windows\System32\spool\PRINTERS\ and I will find it has some ridiculous # of files. Register 4 in Saratoga just had over 50,000 files (which is why I am thinking of this now).
Another visual clue is the user keeps trying to launch RDP and eventually they all trigger and they have a dozen login windows open.
When this happens I clear it either at the command prompt or I have a bat file which I have always intended on installing on the PCs but...
The contents of the file are below. It takes a minute to run and the PC is ready to go for a # of months.
net stop spooler
del /F /q C:\Windows\System32\spool\PRINTERS\*.*
net start spooler
Ben Parker
Northshire Bookstore