Black vinyl couch is seat cover is cracking and pealing
You may be able to save it for a while, but eventually it will all peel. It will need to have Loose covers or Stretch Covers or be Upholstered or re-placed.
I believe there is a spray available (Plasti-? which may be an idea short term.
I saw a post on Apartment Therapy or something similar a while back & they tested several different brands..they ended up recommending Rust-oleum Specialty Vinyl
Unfortunately, peeling vinyl can not be restored.