Threat Management Gateway 2010 is killing SQL Connections
Solution 1:
I finally managed to solve the issue with the help of Microsoft support. It appears that while the TMG server was receiving keep-alive packets from SSMS, TMG wasn't forwarding those packets onto SQL Azure.
I have written a blog post about the problem in full with the vb scripts that Microsoft gave me to run.
http://www.danrowlands.co.uk/2012/03/sql-connections-timing-out-with-tmg.html