Good morning Vasilis,
Perhaps this is also related:
https://www.3cx.com/community/threads/wordpress-live-chat-hours.84715/
I did some more testing and it would seem there is something happening with caching.
When I change the times in the settings of the chat plugin OR the real time changes so that the chat should go online or offline (eg. the chat is online from 9 to 17 hours, it's 8:59 now and the time changes to 9:00 hours OR I manually change the settings so that the chat opens at 8:30), it doesn't do this.
When I reload the page, the chat stays offline or online, whatever it is 'stuck' on.
Even the next day, when one would say the 'cache has expired', the chat is still stuck.
When I open another browser entirely, it does show the correct status until it also gets stuck
The fact that not a lot of people are reporting this, probably means there is something else going on. I don't have a particular caching-plugin installed or something, but perhaps something is going on server-side.
I assumed the check for time opened/closed was done client side in the JS, but I'm now guessing that check is done server side?
I'll dig some more into our own server, thanks for your reply. If I discover anything more, I will report back of course.