Examine the hinges. Open the doors and take a close look at the hinges at the tops of the doors to see if they have worked their way loose. Retighten the screws so that the hinge is seated tightly in the mortise, and then see if the doors swing freely without wiggling around.
Replace the hinge screws with longer screws to pull the doors back into alignment if the hinges are not seated securely. If the doors are too far apart for the latch to catch, loosen the hinges and insert wooden or plastic shims between the hinge and the mortise to move the doors a little closer together.
Loosen the screws on the strike plate and the latch a few turns and then adjust the doors to see if they latch. Insert small shims between the mortise and the strike plate if necessary. Replace the strike plate and the latch with a larger set if they are still a little too far apart or if they are worn.
Reposition the strike plate, if necessary. If the latch and strike plate must be realigned, fill the holes with wood putty and wait for it to dry thoroughly according to the manufacturer's directions before drilling new holes. You may need to chisel out some of the mortise to make adjustments to the strike plate and latch.