The picture below shows my version of a much stronger bracket made from from a PVC plumbing cap.
The second picture shows the failed "builder's special" bracket.
Step 1: Getting Started
You will need (2) 1 1/4" PVC plumbing caps.
There are a few style caps to be aware of. The one pictured below is called a Plug and has a facetted flange around the base. The third photo shows two other style caps - a flat top cap and a domed top cap.
I used the plug only because my hardware store was out of the flat top cap. Either will work just fine. Just don't use the domed cap because the rounded top won't sit flat against the wall.
Step 2: Attachment Hole
Step 3: Cradle Bracket
To create the cradle bracket measure approximatly 1 1/4" across the opening of the cap and make two marks. This is where two cuts will be made to create a clearance cutout for the rod to drop into the cradle.
This only needs to be done for one cap. The other cap is the "fixed end cup" bracket and remains whole.
Step 4: Cuts 1&2
Step 5: Cut 3
Remove the section of the wall.
Step 6: Smooth Edges
Use a file to widen the cutout if necessary, and to smooth the edges.
Step 7: Screw & Washer
(The difference between a regular washer and a fender washer is that the fender washer has a significantly larger outer diameter than a regular washer.)
Step 8: Attach the Brackets
Unfortunately, the new bracket is a smaller diameter than the original; creating a ring of unpainted wood that needs to be touched-up. (As if anyone would even notice that in a dark closet)
Note: This "fixed end cup" bracket was made from a PVC flat top cap. It has a cleaner look without the faceted flange found on the PVC Plug. The plug or the cap work fine for either bracket. Use what you can find in your local hardware store.
Step 9: Finished - Hang It Up!
Insert the closet rod dowel into the fixed end bracket and then drop it into the cradle.
Note: because these brackets are more robust, the closet rod may have be shortened a quarter inch or so, to a fit between the thicker brackets.
These brackets are strong enough to hold up the most clothes one could possibly over-stuff in a closet. Now I've got to work on that sagging metal center support.