It's not uncommon for the stub on the fixing plate for bath/hand towels fixing plates to break off. Unfortunately there are no spare parts available as each type is unique by brand. Due to the weight of hanging and pulling towels on/off the rail, metal glues are just not strong enough. And since there is no common standard in rail lengths, then finding a replacement that will fit in exactly the same spot is not highly unlikely. So, what's the solution?
Though difficult to find for small jobs, a metal engineer could either make up a new plate or spot-weld the stub back on. Or you could fix it yourself. It's not the easiest of DIY projects but doable all the same. Here's how I've done it.

Steps
Step 1
First measure the length and width of the broken stub and buy a bolt as close as possible. The width is the most important.
Then drill through the centre of the broken plate with metal drill bit.


Step 2
Insert the bolt and mark the length to that of the broken stub.
use a vice or vice grips to secure the bolt and cut it to length with the angle grinder.

Step 3
Measure the distance and depth of the notch the locking grub screw on the stub.
Reinsert the bolt through the plate and mark the location on the notch.
Secure the bolt in a vice or vice-grips. Then use an the angle grinder or hacksaw to very carefully make a notch in the bolt

Step 4
Refit the bolt and use an epoxy glue to secure it into place.

Step 5
If the head of the bolt protrudes the depth of the plate, you will need to make a shallow cavity in the tile to prevent the mounting plate from sitting flat.
Use a 12mm multi-purpose bit to make a shallow indent in the centre of where the mounting plate is positioned.

Step 6
Refit the mounting plate to the wall, then the bath/hand towel and you're done.

