OK so we've found the problem, which it's worth noting for the future.
This mail server is a virtual machine, running on a VMWare cluster. Yesterday at around midday, there was a fault on the Host machine that the VM was running on, where the network connection between the server and the SAN became faulty. It didn't fail outright, just became intermittent. So writes to disk were not always completing.
What happened to Argosoft was that it was receiving email, noting it in the database, but then failing to write the physical file to the inbox folder. So when a POP session requested that email by it's UID, Argosoft couldn't find a corresponding .eml file with the correct UIDL, hence the error "invalid parameters".
By looking in Argosoft logs, and comparing to the content of the database table, we have been able to identify the missing UIDLs and add blank text files in the inboxes with the correct filename, which has cured the issue.
Thanks for your help Archie,