I ran into this issue a week or two ago when launching he Exchange Management Console (ESM) for Exchange 2010. As a work-around, I would connect directly to an Exchange server and access ESM from there but given how regularly I do administration work in Exchange I got fed up with the constant logging in and finally fixed the issue.
I did some googling and found a blog that advised me to remove a specific registry entry.
Specifically, this one:
It worked perfectly, so, many thanks to J.W. Koebel for the info found here: http://blog.kf7lze.net/2012/09/21/exchange-server-2010-management-console-cant-connect/.
If you’ve stumbled upon my blog and found that the above advice did not resolve your problem, you might want to try some of the things suggested here: http://terenceluk.blogspot.com/2011/08/unable-to-open-exchange-server-2010s.html