Me and another user in my business use eM client and we have found that with a shared email address, if he archives and email it very often does not reflect this on my client for multiple days.
For instance he’s sitting with 3 emails with the inbox tag, and I’m sitting with 14 - looking at his client & on Gmail they are indeed archived but I’m still seeing them in eM client as if they have not been.
There was an issue like this where a few users experienced a similar thing with some older version 9 releases. First, upgrade to the latest version which you can get here.
Or, if you already have that, or when the upgrade is complete, right-click on the Gmail All Mail folder and choose Properties > Repair > Repair.
Upgraded it and did the repair as suggested and this immediately fixed it. Hoping this will fix it going forward but will report back if it continues happening after this point.