My suggestion would be either to burn the songs before you delete them or else, move them to a folder such as a music folder before you add them to wmp. If not using wmp then just manually add them to your burner program. Oh for wmp see Using windows media player if it's any help at all.
Remember there's other programs that can do the job like iTunes

Remember a playlist is simply a file with a list of titles that points to the location of the song. So if you later move or delete the song after you created the playlist then it won't work!!!