Are those other two computers using a wireless connection by chance, or accessing the backend over a WAN as opposed to a LAN? Is this an Access backend or are you connecting to SQL Server or some other database?
Long running queries can throw Access into a non-responsive state, and - depending on how bad it is - can take hours to run, but they eventually will complete. Thus, I'm not sure about "never completes" or is it "takes a really really long time to complete"
If there's an error of some sort, Ridders suggestion would be my starting point. If it just takes forever but no real error, it could just be a slow connection.
Do you call any VBA code in your query? If so, try putting a static counter in there and debugging out to the immediate window the current count for each time the procedure is hit. That should open up some insight as to whether it's completely hanging or whether it's just excruciatingly slow (don't forget a DoEvents so the immediate window has time to refresh between calls, otherwise it'll look like nothing's happening)