I get logged out also sometimes. I think its part of the new update that it does this, but on topic I don't have a problem logging in. I mean it is a completely new client and there are going to be issues
your problem sounds like
http://forums.steampowered.com/forums/showthread.php?t=1245044
or this
http://forums.steampowered.com/forums/showthread.php?t=1245074
Can you confirm this?