To get a better feel for it, get hold of a beaded necklace (like the ones they fling around at Mardi Gras). Lay it out flat and straight. Twist the two strands together at one point, then let go. They'll stay together. If you try to pull them apart, likely nothing will happen; you have to untwist them in exactly the same way, at the same point. Now, do the same thing with a slinky. The reason that undoing it again is harder, is that where they intertwine wanders up and down the slinky as the spirals shift against each other. However, if you pull apart what you can, you'll find that there are a few specific points (or, in the case you're describing, one specific point) where they're actually locked together. Treat each end of the slinky, from the last knot onwards, like a giant bead. Twist them around each other in the right direction, and they'll come right apart.
Any other ideas?