Try using a primer to keep your eyeshadow in place. I use the Urban Decay one and it's fantastic - last weekend I walked out of the sweatiest, danciest night out you can imagine with all my eye make up still intact
That's mental! My make up stays on all day and requires scrubbing to remove at night! I suspect it may be to do with how oily your skin is. Mine is quite dry. That said i put my make up on over copious amounts of moisturiser and it still does not slide anywhere.
Are you wearing foundation? Or even a powder, as if you dont, your skin will 'eat' your makeup - it needs a base to sit on, and coverstick is too thick for the eye region IMO. It's more for spots.. I'd try a foundation or something first, and make sure you are wearing the right moisturiser - one that isnt too heavy or making your skin look greasy. That would also account for the makeup 'sliding' off. Good luck.