It looks like there isn't any "rule" regarding the fact of opening two Steam sessions from the same computer, I had the occasion to note the following behaviors on the beta client:

• Session break (but the client is working)
• No change on already opened sessions

Could give some details?

• Do you use Steam beta client?
• Is your OS up to date?
• Do you use an administrator session?

Sorry for late answer.
No beta Steam, OS up do date, Win 7 64, no admin session, but never got rights problem. I'm not using two steam sessions!
Just to be clear, it worked before, and it work now.
It happened, because I wanted to install a dev branch version of Arma 3 using the game updater, and while it was downloading, I got a problem with my connexion. Them I can't remember what I did, but I kill all the related process I think, steam, arma, and game updater. And then I got them problem.
After that, I tried everything, it still didn't work. Finally, I deleted the Game updater folder, updated the Arma 3 tools cache, reinstalled the arma 3 tools, and after a while, it worked again...

The fact you're not using two Steam sessions is questionable because Game Updater opens a session to verify that you own the game and download it ;)

Anyway, I will see if I can enhance the handling of connection loss during the update process.

Thanks for the feedback ;)

Note: To restore the initial state of Game Updater, you can use the archive "GameUpdater_files.zip" as described in its read me.

Closed - This is not a bug, Steam must be closed before process or restarted after the update process.

http://feedback.arma3.com/view.php?id=20418#c79704