Problem exporting a video

As a test, create an ISO instead of going directly to disk, then use ImgBurn to write the ISO to disc

If that doesn't work, you have a problem with the drive and/or operating system

https://www.imgburn.com/ to write the ISO to disc (send the author a PayPal donation if you like his program - DO be sure to uncheck anything you don't want from the download site) You may also use Imgburn for general backup of files or folders to disc

You didn't say which Premiere Elements you have or what operating system you use.  (On edit, I see you did give the version.  And, the assumption becomes that to see a burner at all, you are on Windows.)

DVD burners can be tricky.  Premiere Elements has to comunicate with the operating system, then that has to use the burner's driver for the connection to the burner itself.  Add to that the variety and quality of the blanks you buy.

My guess would be that during routine operating system security updates, the DVD driver lost functionality.  Try finding a fresh and current driver from the manufacturer.   

Mine stopped working after a Windows 10 update and I never could get it fixed.   I used it as an excuse to move on to better forms of sharing my videos that have higher image quality.