Turn the table upside down flat on the floor and check the screws for the faulty drop leaf. Put in a new screw if one is missing and tighten. Plug the hole where the screw is located with a rawlplug or wood putty if it has widened.
Unscrew the supports under the drop leaf that is faulty and remove any worn supports. Screw in the new supports using the original holes. Insert rawlplugs or some wood putty to make the holes smaller if these holes are worn or too large to use. Turn the table upright and test the leaf. Apply WD-40 if it appears a little stiff in movement.
Examine the actual table leaf for dents or damage as this can cause problems. Replace the table leaf altogether if it is too damaged to use. Use the old supports and screws and measure carefully to match the opposite leaf so the table is balanced correctly. Drill holes using a smaller bit than the size of the screw and attach old supports exactly opposite the ones on the other side of the table.
Purchase a new table leaf from the original manufacturer if possible or you could make your own. Find a similar one at a garage sale or thrift shop and use a leaf from that. Buying a whole new drop leaf table may work out to be less expensive in the end.