What version of Outlook is this? Does this happen to all users or just a few users? It also sounds like you are using POP for the setup in Outlook. As far as I am aware and I'm not an Outlook expert, but from what I recall Outlook keeps a database record of all emails that were downloaded. This almost sounds like an Outlook issue. What version of SmarterMail are you using?

From time to time we see our Exchange Active Sync (EAS) accounts re-sync without explanation. Sometimes it's after a new version. Sometimes it's when connecting to an EAS/Outlook laptop to a new wi-fi network. Support has never really been able to determine why other than EAS support in Smarter Mail and interoperability with Outlook 2013 and 2016 has been spotty to-date.