Dresser drawers are wooden structures with a plywood base. The plywood base sits in grooves on the sides, front, and rear of the drawer. Time and humidity causes the plywood base to begin to warp creating the appearance of a saggy drawer. Repairing a sagging drawer is a simple matter of reinforcing the base of the drawer. The hardest part of the project is measuring. The measurements must be precise, so measure twice before making any cuts.
Remove the drawer and place it upside down on a flat surface. Press the plywood base back into the grooves along the sides, front, and rear of the drawer.
Measure from side to side on the drawer. Cut a wood board to the width of the drawer with a mitre saw. The board needs to fit beneath the plywood base. Most drawers have a 1/2-inch clearance, while others may have less clearance. Measure the depth of the clearance and use a wood board that is the proper depth if the clearance is less than a half inch.
Pour a bead of glue stretching from one side of the drawer to the other. Press the board from Step 2 onto the bead of glue and secure it in place with clamps. You will have to get creative on how to hold the wood board in place with the clamps. A large piece of scrap wood pressed onto the opposite side of the plywood base will give you some clearance allowing you to clamp the structure from outside the drawer. The purpose is to hold the plywood plank tight against the wood board as the glue dries.
Shoot 1-inch brads at an angle through the ends of the wood board into the sides of the drawers with a brad nailer.
Remove the clamps after the glue has dried according to the drying times listed on the bottle of glue.
An alternative would be to replace the plywood base. You can carefully remove the back of the drawer using a pry bar or hammer, and slide the plywood base out. Cut a new one to the same size and insert it into the drawer. Use a brad nailer to reattach the back to the drawer. Removing the back, however, can weaken the strength of the drawer.