I'm unable to run it due to the inputs not being in the package (please do be cognizant of any confidential data before uploading).
If the same exact inputs work on desktop and not on the server, is there anything in the workflow messages on the gallery that stand-out? You might be able to trace through and see where the records stop processing.
Understood, but when you go to the workflow's page on the gallery you should see a list of all the prior runs. If you expand it, you should see all the workflow messages in detail. Anything out of the ordinary there?
adding to @Luke_C's point, after you run the workflow, if you click back onto the workflow page, at the bottom there should be a table of recent runs. If you click the little down triangle on the left, you should get a lot more information about the tools in the workflow and what happened when you ran it. This should help a lot in diagnosing :)