I have a similar problem with Google - all my analytics accounts are linked to my pro email address, and my gmail is with, er, my gmail address. So I spend the day logging in and out. Would love to be able to consolidate the two.
Google allows for multiple logins. I have one pro gmail account and one personal, and I'm signed on in both at the same time, all day. From time to time I get logged off of one or another, but it works quite well overall.
This just seems to be cookies that expire. Even with one account you have to sign in again once every blue moon.