why are users logged out after 2 days of not logging in
The answer here explains the difference between the cookie types and when they destroy the session: Why is session.cookie_lifetime set to 23 days?

To answer your question specifically:

If you extend the session.cookie_lifetime to be longer, the session will last longer and users will less frequently require to login. If the user opens the page within session.cookie_lifetime from the last visit, the session will be extended for another session.cookie_lifetime. This can be repeated several times, but never longer then session.gc_maxlifetime after which a user is always forced to log in again.

If you extend the session.cookie_lifetime to last for eg. 4 days (so it survives the weekend), users that always open the page on workdays will have to login once every 23 days (session.gc_maxlifetime). You can also extend this value to last as long as you want.

Please keep in mind that although hitting the enter might be annoying, if security is part of your job as well, it might not be a good idea to have sessions lasting for long periods of time. Have them survive the weekend by having them last a day longer will not cause much problems, but allowing them to extend for ever and ever (session.gc_maxlifetime) could introduce security vulnerabilities.