Sounds like you are working glass or obsidian. End snap is part of the game with that stuff. Try not to thin from the base. In other words, thin from the sides. And make sure all platforms are below the centerline of the workpiece.
When a stone snaps in a place where you didn't hit it, it's cased by bending stress. If it snaps right where you hit it, it's caused by a crack that spreads in the wrong direction. Either way, it means you are applying too much force.