Henrik, usual users are not able to enter the site, when it is under maintenance mode, even though they get a message "authentication success" they still cannot leave maintenance page. 

Please test it on your website. 

Create a test profile, under admin, put your site under maintenance and try to login as a test user. 

Okay, now I have done some experiments with a test user. I still think this is a bug, but it is not as severe as I first thought. This is a how I managed to reproduce the problem:

1. I created a test user and logged in to my site using my phone.

2. I logged in as admin from my computer and put my site into maintenance mode.

3. I closed the web browser on my phone without leaving the site.

4. I waited for half an hour.

5: I loaded mysite.com/users as admin on my computer. The test user didn't seem to be online.

6. I restarted the web browser on my phone. When it tried to reload the last page, the maintenance page showed up.

7. I loaded mysite.com/users as admin on my computer. The test user now seemed to be online.

I guess this means that even though users may turn up as logged in on the mysite.com/users page while the site is in maintenance mode, they cannot do anything else than changing their status from logged out to logged in.

Yes, the users stays online on users listing, however the user himself, does not see anything but maintenance page. 

After 30 minutes of inactivity the users is automatically logged out. 

If he is not, that means your cron is not properly configured. Please do the search on the forum regarding the issues with users staying online and cron configuration

This topic has already been discussed many times. 

No, that is not my point. My test user is indeed logged out after 30 minutes of inactivity. The point is that when he eventually tries to do something - and this may be several hours later - the site once again register him as logged in, even though the site is still in maintenance mode. The test user is met by the maintenance page and cannot do anything, but it may still be confusing for an admin that a user suddenly seems to be online again.

I'm sorry but I really don't see any issue here. 

What do you mean when he eventually do something several hours later - what can this user do if he ends up on maintenance page everytime he tries your website, until you disable maintenance mode. 

He may for example try to reload the page he is viewing. This will send him to the maintenance page, which is a good thing. However, it will also change his status from logged out to logged in, which is not a good thing since it may scare an admin currently doing maintenance on the site.

you can make a suggestion on uservoice: https://oxwall.uservoice.com/forums/13756-ideas-for-oxwall

if it gets enough voices we'll consider changin this behavior. in the meantime this is considered as a custom code modification, you will need to do that on your own or hire a programmer to do that for you, you can do that here: http://www.oxwall.org/market/specialists

Okay, thanks. I'll settle by contributing with this thread. Hopefully other admins who get confused by this strange behavior will find this thread and get reassured.