Hello!
It's been a while since my issue has started to happen.
I can't give to someone a temp rank because it lasts forever after rejoin. Screenshots will describe it in the best way.

So this is how /lp user ... parent info looks like before I do anything.

Now I will give a temp group to a player with command /lp user tester parent addtemp mvip 1m and here is the output of /lp user ... parent info:

Everything seems to be okay, but now I will rejoin to the server with the tester account.

Output of the /lp user ... parent info after rejoin:

Here we can see that the test account has a group mvip which will never expire.

And finally Output of the /lp user ... parent info when the group should expire:

I've noticed that when a player is online the group will expire after a certain time (even this one which is forever), but when someone is offline and his/her group should expire it only removes a temp group and the second one lasts forever.

Here is some information about my lp configuration:
Lobby:

Survival:

Skyblock:

Another server:

Bungee:

All servers are connected to one MySQL database. Can you please help me with this, because it is so frustrating :c

EDIT:
I've updated to the latest version of LP on every server and it still happens. What's more I've noticed that it doesn't remove the "forever" group even when a player is online.

Can you try to reproduce this on a server with no plugins other than LuckPerms?

I will do it today or tomorrow. Should I connect this server to my bungee network or run in standalone only with the same MysSQL database?

Okay, so I've fixed this problem. It was caused by authme option called "GroupOptions". It deletes all groups to protect some exploits (now I use Authmebridge) and after login gives it back, but it remembers a temp group as a forever group.
Anyway I appreciate your will of help! Thank you very much and sorry for wasting your time!

No worries, glad you found the problem!