The key to repairing a sagging couch with non-removable cushions is the cushions themselves. The two ways of dealing with them are to either remove the fabric and completely reupholster and support the couch or pry up the cushions and replace them in such a way that the sagging is minimal. Either option is acceptable based only on the amount of work that the repairer wants to undertake on this particular piece of furniture. Since most couches that are sagging are likely to require fabric replacement as well, replacing the entire couch fabric now may save you from doing additional repairs in the future.
Saving the Old Fabric
Spread open the crack behind the couch cushions. Cut along the crack as deeply as possible in a location where it is the least noticeable. Spread the fabric apart and look inside the couch. Sever the couch cushions from their interior attachments if necessary.
Slide a plywood board the same size as the seat of the couch in through the hole in the fabric and underneath the cushions. Arrange the plywood so that it is evenly situated and cannot be felt by someone sitting on the couch. Cut the plywood smaller if necessary so it does not protrude beyond the cushions.
Close the cut in the fabric by securing it with safety pins along the length of the cut then shove the cut deeply into the crack behind the cushions and pin it down to make it less noticeable.
Replacing the Couch Fabric
Flip the couch upside down and pull all of the staples out of the base, ripping any seams if necessary or cutting the fabric with scissors to remove it. Continue to remove the fabric from the entire couch by pulling staples, ripping seams and cutting fabric. Pull up the cushions, cutting them from their attachments if necessary and slide a plywood board the same size as the cushion area underneath the cushions.
Spread out the fabric and measure it. Cut a new piece of fabric for the couch that is at least one full yard larger than the old fabric. Lower it over the couch and loosely position it so that it covers the entire couch. Attach it in the cracks around the cushions with staples while stretching the fabric tightly.
Continue to stretch the fabric taut over the sides, front and back of the couch, stapling whenever possible in inconspicuous areas. Flip over the couch and staple the fabric to the base of the couch about 2 inches in from the edge all the way around, stapling every 4 inches. Cut out any extra fabric with the scissors.