Copying large files I get the error “Insufficient system resources exist to complete the requested service”

The only thing that springs to mind that might be a generic issue rather than one specific to ThirdPartyApplication(tm) is that if the machine it is reading the file from does not have sufficient client access licenses. With server editions it depends how you have the licensing configured and what licenses you have (for XP there is a fixed limit of 10 concurrent connections if I remember rightly). I have seen connections get "hung" in some cases on XP, such that no new file sharing connections can be opened until XP is restarted, though I have never seen this on a server edition, so the old faithful solution of restarting Windows may be a quick-fix work-around until you can find a more permanent solution.

If it isn't a licensing issue then you should probably contact the creators of that third party application as your first resort: they may be aware of a possible issue and already know how to fix or work around it.

ps. for questions such as this, it is helpful to specify the exact Windows version+variant that is installed on both machines, and what the third party application in question actually is - then if by chance someone else has hit the exact same problem previously you might get a quicker (more accurate) answer.

Can you just rebuild it from scratch and reinstall EPO? Might be the easier option.