I have exactly the same problem. For months everything was working fine. I m not an expert, that is why I hoped Mailerlite would help me to solve the problem (NOT!!!).
I have the feeling it started after updating to WordPress 5.6.x
Since then the problems started.
Now I see that the plugin says “Tested till 5.5.3” and last update “3 months ago”. This is a bit strange to me for a company like this.
Then I start to worry that this company is in some kind of problems of whatever and they might dissappear soon.
Support answered me with a one liner: disable all plugins.
What is not helping by the way, and what I ofcourse tried myself before contacting support.
So, before you swith from any mail client to Mailerlite, think twice.