Add a piece of material sufficiently long as to fit beneath a seat cushion. The length of the arm cover should be so long as to be able to fit behind a seat back cushion.
Thanks for your reply. Unfortunately, the cushions are not removable. The sofa has recliners on each end. Sorry, I should have added that information.
I'm thinking you might be able to put a piece of the rubber backing material that holds rugs in place. You can purchase it in a roll or rug size. Here's an Amazon link to take a look at:
Heavy duty velcro strips