There are a couple of things you can try when the lava won't stick to a coil. The easiest thing to try is to turn off the lamp after it's been running a few hours and spin the globe back and forth to try and get the lava to reconnect with the coil. Sometimes, this will work. Sometimes, it will work temporarily only to become detached again.
If the coil itself is bad, you can try to clean the coil by draining (and saving) the wax and fluid. Soak the coil in a degreaser (found at your local hardware/home improvement store) for 24 hours and gently scrub/rinse the coil clean before reassembling your lamp.
If the coil is shot entirely (bad coil, or it's just old/rusty/etc) you can attempt to replace the coil by purchasing a new one at a hardware/home improvement store. Best material for coils will be stainless steel. Vintage coils had a wire size of about .014" thick and a diameter 5/16" thick. The length of coil for a 32oz. globe is about 5.5" long, but if you find a shorter coil, it can be stretched a little.
For additional information about coils, look here.