For the back of the chair I made a cover like a big pillow case that slides over it stays put and comes off to be washed. the arms are harder to keep covers on but the one with ties together at the back works..

You can purchase the non-skid shelving in large 12" strips for a small amount. This sounds like a lot but I did go to what we have (not sure if available in your area) but it's a Yoga mat made out of the same non-skid shelving material, just heavier. Might find it in dollar stores. But it's wider and bigger and a bit stronger. it's wide enough to fit the back and arms of the chair.

By the way mine also have pockets to hold my remote. They are long so you tuck them in. Mine are on my recliner and I have no problems with them slipping or coming loose.

Try the rubber fabric they sell for little kids PJ, they are heavy and you could do a fancy stitch to attach to back of material.

As I sit here in my reliner straightening the arm covers........I like the idea of tieing them to the back. Hmmmmm.

I use T pins bought at Joanns.

My mom uses hand towels that match the chair. She puts them on with a bit of it hanging over the front of the arm. Then she folds the "hang over" part so that it is form fitting to the chair arm. (Sort of like the darts in dresses of the 60's.) She pins the "darts" and then stitches them down. Works great. Hope I explained it okay.

Just what I was thinking

Terry cloth hand towels, then Put rows of hot glue on the slip cover , allow to dry then use. its acts like grippers olding the cover in place.

Would elastic strips also work?