It seems that Steam had finally calmed down after the big update, we will reboot our servers in an hour and hopefully this will clear up all the remaining connection issues.
US servers will be rebooted at 12:00am on September 8 (PST)
European servers will be rebooted at 9:00am on September 8 (CET)
The servers should be back online in about 15 minutes, please let us know of any connection issues after the reboot is completed.