Stickiness that won't come off

I've been having a problem with some of my pots and pans (more importantly, my Le Creuset dutch oven) where there is some kind of stickiness that just won't wash off. It is colorless, and has seemed to appear out of nowhere.
I've tried dish soap and water, even using the dishwasher powder to make an abrasive paste but still cannot remove it. Thankfully it is on the outside of the pieces, but it would be nice not to have my hand stick to it when I try and put it away.
Has anyone else had this problem/figured out a way to solve it?

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