Within Linux, these functionalities are provided by a package called autossh. Something equivalent to this exists in Windows too, even though not through the ever-popular Putty application.
On the one hand, there is autossh within Cygwin. This is extremely close to the Linux code, and you can find instructions on how to set it up here. The upside of this is the very same as its downside: you have to install Cygwin. Cygwin is a fantastic program, aimed at recreating a Posix-compliant environment inside Windows. Many people use it daily, but if you do not have specific needs, you may find as excessively complicated to achieve an otherwise attainable goal. Still, if you are into greatly improving your ability to do things inside Windows, I warmly recommend it.
A more agile alternative is MyEnTunnel (=My Encrypted Tunnel). MyEnTunnel
uses PLink to monitor the connection to a remote side. Should this fail, it will automatically reconnect.
The cute thing about MyEnTunnel is that is not disjoint from Putty: as a matter of fact, it can also use Putty sessions, a nd Putty-generated cryptographic keys. Which, in my view, is a definite advantage if you are already using Putty.