I found the answer to this. It has to do with a registry entry. If the server is created using a template, such as our vm servers, or was cloned with cloning software, then we have to go delete two registry keys. This is because the keys already exist on the original server and are cloned as is to the new server. They have to be deleted.
They are found here
The keys to delete are SusClientId and SusClientIdValidation.
Next I delete the server names from the WSUS console.
Once these are deleted then I ran wuauclt /resetauthorization and wuauclt /detectnow. The keys are automatically regenerated in the registry and the servers show up in WSUS and don’t “disappear” any more.