I solved this way: updated theme, deactivated all third party plugins, updated all related to WPLMS plugins, cleared browser cache. After that I enabled - one by one other plugins checking, if they do not affect the WPLMS.
Maybe it is important or not (I do not know), but I have to wait about few hours to see that all is ok. I did as I wrote above, wait some time, and it was working.
As I read, Vibe support advices to clear server cache, not only browser in some cases. To do it you have to look, in which folder on server there are .cache Wordpress files (look at Wordpress official site and clear cache with FTP client, if you use it).
Please follow the steps mentioned by @szmaragd carefully .
it helped many users .Sometimes server also caches the scripts and pages which caused these kind if issues .
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