I’ve always used two (Chrome) tabs for two different Google Apps Email accounts.  For some reason this morning it wouldn’t let me do this, it would sign me out of one before I could use another.

A fix for this seems to be: visit https://www.google.com/accounts, choose ‘Multiple Sign-in’; then click on the drop down arrow on the top right, add the other account and you seem to be able to use different google accounts in different tabs again.

Not sure what they changed, but this seems to work.  You can also use an ‘icognitio’ window according to one blog.