Lately, we get a communication error at some point during the day (could be to any of the 4 users), and although we can continue to use the file as usual, at the end of the day, after only one person remains logged in, we get the message "you must be the only person logged in to back up" and we can't back up. The only way we have found to get it to back up is to restart the server where the file resides, re-log on as one of the users, then log out and back up.

Very annoying, and obviously something we'd like to prevent/fix.

Any clue? We use AccountEdge 2005 and Mac OS X.

It sounds like you have a lock file on the server. This can happen if any one of your users are not logging out of the file when they shut their computer down. If one of the users are also using a screen saver or let the computer go to sleep instead of shutting down.
If everyone is logged out and a lock file still remain, just delete the lock file.

Is the locked file found in the same folder as the data file? (not at the office right now, so can't look)

yes, there may also be access files. If so, then delete them as well.