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There are different ways of fastening this type of fixture, depending on the fixture itself and the wall material. First, you will have to take the towel bars down to see why the failure is occurring.
Fixtures on ceramic tile are installed in two ways. In the good old days, they were set into plaster as part of the tile job. More recently, most installations are surface mounts, with the ceramic fixtures mounting on the surface of the tile by means of metal brackets.
It's easy enough to tell if the fixture is mounted on a bracket. Just look underneath the fixture. You'll see the grooves and hollow space underneath where the metal bracket slides in. Tapping gently upwards with a block of wood or rubber mallet should release the fixture from the bracket.
(1) If the fixture is set in plaster...
Plaster failure will require you to remove the fixtures from the wall and reset them in plaster of Paris or construction adhesive. If the plaster in the wall is still solid and only the fixture released, you can probably use construction adhesive. Remove any dust before gluing and be sure both surfaces are dry. Use as much adhesive as you can without causing it to squeeze out from the back of the fixture. Prop up the fixture to keep it in position until the adhesive dries. Use your imagination… masking tape or a carefully cut board are two possibilities. Whatever you use, put something soft on the floor beneath the ceramic fixture just in case it falls. You will probably never get a match in color or size if this one crashes!
If, in your judgment, there is not enough plaster backing for adhesive to work, mix up a batch of plaster of Paris... at least a few cups... and slather it thickly onto the wall and the fixture. Press the fixture back into place and wipe off all the excess plaster before it firms up... within 5 or so minutes depending on the temperature. Prop the fixture in place until the plaster sets hard... at least an hour or so. Don't stress it for at least 24 hours.
(2) If the fixture is held up by anchors...
If the fixtures are held up by anchors, chances are the existing wall anchors are not the right type, and tightening will not be effective. Instead, the anchors have to be upgraded to a sturdier type. If the original anchors are plastic expansion anchors, you can install Molly bolts in their place. Molly bolts are metal anchors that expand in the wall as the screw is tightened. The strongest installation would be with toggle bolts. Toggles are spring loaded and open inside the wall.
If you are unfamiliar with these anchors, take the bar and/or base plate to the hardware store and ask to see these types of anchors. Hopefully the store personnel can give you hands on help.