Latest development:
Support replied to me today
"we are still working on a fix but there is a workaround which worked for couple of users. Can you please test it and let me know if that worked for you, too?
1. go to menu > settings > general > general
2. if the option “empty trash on exit” is checked, please uncheck it
3. try to replicate the issue."
This workaround - I tried all day today closing and opening eM Client - actually seems to work for me. You should try it as well. It seems, eM Client developers are on the right track now.