This video shows you how to fix a Bungee cord where the elastic has separated from the hook.
Step 1: Limp Bungee Cord
If one side of your bungee cord is floppy, it's because the elastic on the inside has broken free. The first thing to do is feel the cord and determine where the elastic stopped. Then cut the cord with a razor blade or utility knife. Next, cut the excess empty sheathing nearest to the hook.
Step 2: Drill Out the Hole
Put the hook in a vise and use a drill press (with a drill bit slightly larger than the diameter of the cord) to drill out the hole. You may find there's metal embedded in the plastic along with the cord remains, just go slowly. Drill down to where it's just above where the thin part of the hook starts.
Then test fit the cord to see if it fits. If the hole is too tight at the opening, use a countersink bit to widen it up to make insertion easier.
Step 3: Time for Glue
After confirming the cord fits in the hole, put some E6000 glue in the hole and twist the cord inside. The twisting will make it easier to insert and also spread the glue around. E6000 is a flexible glue, so it's good for a connection like a rubber bungee. Clamp the bungee cord upright in a vise and add more glue until it circles the top. Try to keep the cord vertical, so it doesn't cure kinked to the side.
Step 4: All Done
Leave the bungee cord overnight and then test it out in the morning. It should stretch and hold just like new!