Princess was really bad about finding something & heading for the hills....it was a big game to her.
I taught her drop it using her ball (most prized possession) for a tiny treat. Now she almost always drops "it" without me saying more than that. I don't pretend to go after her or even shift my position as she'll either run or gulp what she has. It did take a while & still sometimes I have to "lecture" her...("You put that down right now, that is naughty!") but before that's over she'll drop it and I still reward her to remind her that good things come from that.
I think it just may be an ongoing effort for some dogs. The leave it command is even better & safer I think, that way they don't even get the "something" in their mouth. I'd just recommend consistent positive reinforcement & expect for it to take a while unfortunately.
Good luck!
