A towel bar that wiggles can enlarge the mounting hole every time it is used. Tightening it early is usually a small repair, but the fastener must grip something solid and the bracket must be aligned before the decorative cover is replaced.
Remove the cover carefully
Look underneath the escutcheon for a small set screw or gently release the cover according to the design. Support the bar while removing one side so it does not pull the second bracket loose. Put the tiny screw where it cannot roll into the drain.
Inspect the mounting
Check whether the mounting plate is fastened to a stud, a solid blocking point, or a wall anchor. Tighten a loose screw gradually. If the screw spins without gripping, remove it and use a suitable replacement anchor for the wall material rather than forcing a larger screw into a damaged hole.
Reset the bracket
Hold the plate level and mark new holes only when the original location cannot be repaired. Avoid drilling into plumbing or wiring. Install the anchor as directed, tighten until the plate is firm, and stop before deforming the plate or crushing drywall.
Reassemble and test
Replace the cover and set screw, then apply gentle downward pressure to the bar. It should stay still without pulling away from the wall. Do not use a towel bar as a grab bar; if the bathroom needs a support rail, install a product designed for that load with proper structural backing.