If the towel bar is the right length you may be able to mount one, or both of the escutcheons, directly to the wall studs behind the drywall. Use 1 3/4-inch drywall screws to mount the anchor plates.

Towel bars usually come loose because the hole in the drywall becomes elongated and enlarged, and the screw and anchor pop out of the wall. Fortunately, there is a quick and inexpensive answer.