[Dougal]

As chucks wear, they often get bellmouthed. The tips near your cutter end up worn/damaged and don't grip the part, instead the jaws only make contact further in.
This results in a part that will be close to concentric near the jaws, but further out as you get further from the chuck. I think my 3 jaw is getting close to this point.

You can fix that by honing it, I've done it before using a piece of cast-iron, a drill press and grinding paste. But there must be many methods.