When you open the Minecraft Launcher (offline mode), you are logged out.

When I open the Minecraft Launcher, log in and close the Launcher, when I log back in it gives me a login error. You should stay logged in and not log out. (This happens to users who do not have an internet connection and enter the Minecraft Launcher). However, I was testing a Minecraft client called Lunar Client that does keep the session for 24 hours and after that time, the session expires. For which I came to the conclusion that Minecraft Launcher has said bug which closes you the session when you reopen the Launcher.