Rugs, Carpets and Carpeting - pile broken on area rug

we have a long narrow area rug (one of those available at lowes or home depot) and it appears that the back is broken.

As the rug is laid out on the floor the middle tends to stick up at one place creating a tripping hazard. At times the bump can be a couple inches high and I push it down a couple times a day to try and avoid someone tripping over it.

Normally I would replace the carpet but in this economy I would prefer to fix the rug and get more life out of it.

I was wondering if something like carpet tape or something stiffer could be used to reinforce the back of the rug so it would no longer create a tripping hazard.

I haven't tried this for your purposes but in theory it could work. I use it to correct delamination in backings and that is basically reinforcing the carpet so i think it may translate over. Get the wide drywall mesh and run it lengthwise across the section that sticks up. Use a hot glue gun and fill the mesh with hot glue. My glue gun has a wide tip that shoots out about 2-3" wide and i use that to smooth it out across the mesh. If you don't have that you'll want something like a 4" drywall knife to smooth out the hot glue. Make sure the knife is hot so it doesn't cool the glue on contact.

You may have to make 2 or 3 of these splints across the width to get that area that wants to lift stiff enough.