I think I know why this happened from the beginning. I got the warning message in Health Reports about having Admin accounts running the app pools or services. So I have corrected one account and now all these messages are gone. But that caused a new problem with Search Service. The error message was:
Maybe not recommended, but I will keep it running like this. The message in the Health Analyzer has not come back so, so far so good.
“Unable to retrieve topology component health states. This may be because the admin component is not up and running.”