Position the couch upside down and remove the staples that hold the bottom cover onto the couch with a needle nose pliers. Only remove staples from three sides. Lift the cover off the bottom of the couch so you can see the internals.
Locate the broken or cracked board inside the couch that is making the couch sink.
Cut two pieces with a miter saw of 1-inch-thick by 2-inch-wide boards to the same length as the broken board.
Straighten the broken board with your hands so it runs straight.
Apply construction grade adhesive to both sides of the broken board. Clamp the 2-inch face of the boards you cut with clamps. Place a board on each side of the broken board.
Drive 1/4-inch-by-2-inch-long wood screws through the new boards. Place an evenly spaced screw approximately every 6 inches down both sides.
Place the cover over the bottom of the couch. Staple the cover in place with a staple gun.
Remove the cushions from the couch and place off to the side.
Measure from the back of the couch frame where the cushions rest to the front of the couch frame. You do not want the plywood to come to the very front of the couch so subtract two inches from the measurement.
Measure from the left of the couch frame where the cushions rest to the right of the couch frame.
Cut a piece of 1/2-inch thick plywood with a table saw to the dimensions you obtained in Steps 2 and 3.
Drill a 1/4-inch diameter pilot hole through the top of the plywood in each corner.
Place the plywood onto the top of the couch frame and push it back as far as it will go. All four edges of the plywood must rest on the frame of the couch.
Secure the frame to the couch. Drive 1/4-inch-diameter by 2-inch-long wood screws into the pilot holes.
Place the covers on top of the plywood.