You can add a query string the to end of the file name. It will be cached as a separate file, but it will be the same filename. It's basically a forced recache for the file. Just go to the link in the HTML and add something like this:
<link href="path/to/file/site_main61.css?version=1" ... />
This will work with most caching systems and you no longer have to change the file name.