If all your eM Client installations have just started doing that, could be eg: possibly something running resident in the background on the computers causing them to freeze or not respond,
Or possibly your OS might need updating or patching depending on what you have already.
So suggest first to try uninstalling eM Client and if you have Windows “don’t delete the database” when asked on the uninstall wizard.
Then reinstall the same or later version for what you are already currently running for Windows or Mac either via the release history page or Windows Store depending on where you originally installed it from and see if that fixes it.
If that still doesn’t fix it “check you have the latest OS updates” for Windows 10 / 11 or Mac. There has been alot of OS big updates recently.
If you already have the latest OS updates “then for a test”, try disabling all non OS optionally installed user related programs on startup “other than the basic OS stuff” and see if that stops the non responsive issue. You will then know if it’s anything running resident on startup causing the issue.
Apart from that you might possibly have some issue with your local mail database. So if you have an IMAP, Exchange, Office 365, or iCloud account and nothing in Local Folders, “you could try creating a new database to test” and setup new to see if thats the issue.
To do that “first close eM Client” and then rename the following hidden database folder below end of post to eg: eM Client-Old.
Then reopen eM Client & setup new. All your email will then come back from the server when eM Client recconects. Emails will just be slower to reread till fully cached.
(Windows hidden eM Client database folder)
“Users\yourusername\AppData\Roaming\eM Client”
(Mac Hidden hidden eM Client database folder)
“Users\yourusername\Library\Application Support\eM Client”
Lastly once you have it sorted out make a manual backup via “Menu / Backup” to save it.