Page caching and eCommerce have always struggled to work well together. Both technologies have worked hard to overcome the issues with some success, but there are still some issues.
General Issues with EDD and Caching
The Software Licensing extension works by having your software communicate with your EDD store over an API. That Software Licensing endpoint can get cached by any of the common caching plugins. This will cause problems when checking licenses.
The fix for this issue is to simply not cache anything in the Software Licensing directory.
If using WP Rocket you can use this pattern to exclude the proper things: /edd-sl/(.*)
If using WP Super Cache, choose the setting Don’t cache pages with GET parameters. (?x=y at the end of a url)
Specific Issues with Caching Plugins
Each caching plugin has its own issues, here are docs for each one.