I'm assuming that it was held to the wall with plastic anchors and screws?...which is always a recipe for failure. You've got several options for improvement:

1) Move the TP holder so at least one of the wall brackets is into a stud (it looks like there might be a stud next to the holes, because I see what looks like a nail-pop a little to the right of where the bracket was).

2) Use better fasteners, like these threaded anchors: https://www.ronhazelton.com/projects/how_threaded_wall_anchors_are_stronger

3) Get a different TP holder...a single post design that only requires support on one end, and that will allow you to securely mount it into a stud, like this kind: https://www.homedepot.com/p/Delta-Lyndall-Single-Post-Toilet-Paper-Holder-in-Brushed-Nickel-LDL50-SN/205341562

Or patch the holes and install a recessed toilet tissue like this one:

https://www.homedepot.com/p/ARISTA-Recessed-Toilet-Paper-Holder-with-Mounting-Plate-in-Satin-Nickel-RTPH-P-SN/205155858

After my kids tore the towel holders off the wall for the third time I bit the bullet and opened it up enough to put a blocker board behind it so I could screw into wood.

I use a pice of ~1 x 3, slide it into the hole in the plaster, first one end and then the other, hold it in place either with your fingers or a temporary screw to grab, then anchor it to the wall with drywall screws from the outside. Patch the hole and over the drywall screws and you have a solid surface to screw into wherever you need it. I haven't had one of those installations fail yet.

It's easier if you can move it so you can screw into a stud.

Or, you could go this route:

Looks like drywall. Not lathe and plaster.

No matter though, whatever that's attached to the wall needs secured to a stud.

Yes Sambah, I realize it was replaced with drywall during remodel.

I will look for a stud, to put the holder. But will have to patch the 4 holes once moved.

Thanks

whatever that's attached to the wall needs secured to a stud.

That's not true. In a commercial establishment, yes, it would be a good idea. But for your average house, self-drilling nylon anchors will work fine:

Drywall anchors

Funny story: I installed an entire Closet-Maid closet unit using nylon anchors without ever hitting a stud. It's been 10 years and all is fine.

The problem with these anchors is that the holes on the wall are already too wide for the anchor. There is no support to screw them and allow them to expand internally or on the back of the drywall. The screw just slides right it. I tried with a hollow wall anchor I had at home.

like these

I would need a much wider drywall anchor. Do they exist?

Thanks

Yes...they exist in a wide range of sizes. But don't just go for a larger, regular plastic one. Get a threaded anchor like I mentioned in my first response to you several days ago.

Have you seen the screw in anchors? From the looks of your photo, they are larger than the holes in the photo.

What you need is not the screw shaped drywall anchors, but the toggle bolt style anchors that have little wings that expand inside the drywall. Sorry I don't have a photo but I've used these many times and they are very secure. Sometimes they are nylon other times metal. Go to your local big box store and ask for them. I'm sure they have a large display.

Nancy-

A single, typical threaded insert has a pullout strength of at least 80 pounds, so they are entirely adequate for this job as long as the size is properly matched to the hole. The fastener you are talking about -- a molly bolt with a wing nut -- is not as good in my opinion as the nut makes a hole much bigger in diameter than the bolt itself. Over time this can allow something that is used frequently (like a TP holder) to move around a bit and sometimes the bolt loosens. An alternative molly bolt that does not have this problem is a hollow drive molly bolt that does not have a separate nut but consists of a tubular shaft that compresses behind the wall when the bolt is screwed in; the shaft fills the hole so there is no wiggling around of the bolt. However, the hole must match the fastener diameter; if the hole is oversize it can't be properly set. It also has the advantage that you can remove and reinsert the bolt repeatedly since the tube part doesn't fall behind the wall like the single use wing nut style.

I can't find anything with a bigger diameter than the current hole. Most anchors I am finding, go straight through the hole.

Check out the toggler system by Snaptoggle. They are pricey but they work great. You could find a cheaper alternative with metal butterfly anchors but if you have to remove them, you lose the anchor.

Hi, i repaired a few problems like this. It looks like the other end is on a stud.You can use a nice piece of wood or aluminum make sure the material is wider than the tp holder cut the material about 2 inches longer than the tp holder . Drill two small holes in the center of the material and screw it to the stud. Mount the tp holder to the material. Patch the Hole or make the material longer to cover the hole. You may want to make it longer on both ends for visual effect. This works on towel bars too.

Good Luck Woodbutcher