Well, I'm not sure that you've really gotten your answer yet. You say it works sometimes, so it sounds like File & Print Sharing should be installed per the above Q-article. As far as entering the /user:machinename\username, I don't think it will help here since you're getting error 53 (path not found) - it's not having trouble authenticating, its having trouble finding the server.
Error 53 basically means it can't find the server on the other side. I take it that they run the command from their TS session and not from their local client. If so, I would concentrate on name resolution - even though you're typing in the IP address (and you would think that since you just fed it the exact address it wouldn't need the name), NT still needs to know the Netbios name of the box. It has 3 methods of figuring it out and when they all fail, it returns 53. You can assit in the process by feeding the info to the sevrer by adding an entry to the LMHOSTS file on the TS (\winnt\system32\drivers\etc) that looks like this:
192.168.0.1 Servername #PRE
If this server you're mapping to is a Domain controller, add #DOM:yourdomainname to the end of the line. Spacing is not important, just make sure you add some spaces between columns.
LMHOSTS files are poor at scalability and if you ever change ip addresses, this thing will come back to bite you. WINS is a much better solution, but if the operation is small, its no big deal.
Let us know how it goes.