When a request keeps coming back as Awaiting Unfilled Processing, it means there is an open OCLC request associated with that request's Transaction Number. Here are the steps to take to fix this issue:
Another possibility is that a request that came in as Unfilled and was routed to Awaiting Direct Request Sending. This does not delete the old request from OCLC. Before routing the request to the new status, go to the OCLC Request tab and delete the old ILL number first. Then route it to Awaiting Direct Request Sending if desired.
Once you have verified that there are no active OCLC requests for that item, it can then be completed or routed to the next step in your library's workflow.
To avoid this issue, see this Atlas Systems document: Fix Requests that Continuously Return to Awaiting Unfilled Processing.