PuTTY - Automatic Reconnect After Internet Interruption?
Kitty is a forked version of putty that adds reconnect, send to tray and stored username/password. The auto reconnect works after the machine awakes from sleep as well. It's been very stable for me. FREE :)
There's also a fork of PuTTY called PuTTY Tray which adds a "reconnect on connection failure" option (albeit experimental): https://puttytray.goeswhere.com/