Drop leaf tables were very popular several years ago and many are now considered to be antiques, so you may need to repair the leaf on yours. This is a simple job that you can probably accomplish with tools you have around the house.
Step One: Determine the Problem
The drop leaf can be loose or not moving properly for a number of reasons. You will need to get underneath the table to determine what the problem is. If the wooden brace you put in place to hold the leaf up is too loose or missing, you will need to cut a piece of wood at least 8 inches long to replace it. Screw it into place with a wood screw, but don't tighten all the way so the brace can rotate.
If the hinges are loose simply tightening them may fix the problem. Be careful not to tighten too tightly as you can split the wood.
Step Two: Replace the Hinge
If a hinge is badly rusted, damaged or missing you will need to replace it. Table hinges can be purchased at any hardware store inexpensively. Try to mount the new hinge using the holes for the old one. Simply screw the screws into place being careful that the side of the hinge that bends is in the proper position. If the holes don't line up, you will, of course, need to drill new ones.