Well, that's a pretty generic connection termination error. I am still inclined to believe this is an environmental issue (network issue, firewall, other security), particularly since other network connections are working fine. However, you can do a simple test to find out a little more.
When the issue is occuring and putty does not connect, if you can log into the console command line itself (that is, directly at the appliance keyboard), using the admin account, you can try the following command:
telnet localhost 22
SSH should respond with some versioning information. If it does not respond with versioning information, then make sure there are no SSH access rules involved:
sshd-config --list
If there are any access rules listed, it may be part of the issue. You can modify the access rules by using the sshd-config add/delete commands. For more information, use:
sshd-config --help
If there are no access rules listed, and you cannot connect locally, you may be running into system resource issues. I would recommend opening a case with support at that time.