If you previously had the encoder but now no longer do, that's because your driver is reporting back that the encoder doesn't exist. The plugin takes extra care in making sure that everything is how it likes things to be to avoid unnecessary CPU usage.
Also please do not advise to use older versions of the plugin. There are code fixes in newer versions that older versions don't have and we will just end up getting more "bug" reports.
As for what you can try doing is to do a completely clean install of your Driver (remove all GPU drivers, not just AMD ones), disable any other GPUs (if you have them) in your bios and lastly attach a monitor you want to use encoding on.