Our licensing server should recognize that it's still the same computer after you reinstall. However, sometimes, there are problems with Windows that cause our server not to recognize the computer after you make changes. But don't worry. This is easy to fix.
After you reinstall your OS and all your plugins, open a plugin window for one of your PA plugins. You'll need to re-enter your login info. Afterward, go to Devices and check to see if your computer is listed twice. If it is, click "Deactivate" for the older machine. If you can't tell which is the older one, deactivate everything. Then re-authorize your plugins again, and then you should be properly authorized.