Recently we had a client that was having difficulty moving her heavier than usual drapery across the rod to close. The drapes were mounted higher than normal and were made with black out lining.
One spray of jig-a-loo on the rod loosed everything right up. The client emailed us later and said they worked perfectly.
Jig-a-loo is a silicone based lubricant made with no grease, oil, wax, petroleum or detergent. It doesn't stink and won't stain! Sounds perfect!
Works on most things around the house that need unsticking.
Just be careful if you're googling it....and don't use it on people :)
Here, I'll save you the trouble. Visit Jig-a-loo