[Решено] Language switcher disappeared from menu after update

Background of the issue:
I am trying to see the language switcher on the menu. It was activated and still is. Link to a page where the issue can be seen: скрытая ссылка

Symptoms:
The language switcher disappeared from the menu after an update. I have a message in my admin area: 'The WPML plugin can't connect to wpml.org'.

Questions:
Can the connection issue with wpml.org be causing the language switcher to disappear?