Error number 2013 is:
Message: Lost connection to MySQL server during query
according to http://dev.mysql.com/doc/refman/5.0/en/error-handling.html
This topic in the MySQL docs
http://dev.mysql.com/doc/refman/5.0/en/gone-away.html
could prove to have the solution. But you see there are a lot of possibilities.
Questions:
1) You don't try to use any other SSH software than the client that comes with SQLyog (plink.exe in the SQLyog installation directory) ?
2) If you 'test connection' from the connections manager what happens then ?
3) Did you read the help file regarding how to set up the Connections Manager with SHH? The description here is pretty good actually!
4) Couldn't you possibly disable the firewall for 5 seconds? But personally I don't believe that is it. Rather a networking issue on the remote server place involving SSH and MySQL. But that is a guess!