All pencil users have experienced this at some point. The point of your pencil breaks, you sharpen it and it breaks again; repeat until you give up or it’s all gone.
The reason this happens is usually because the pencil lead is broken on the inside. When I feel like that is the problem I just throw it out and get anohter pencil.
Other times there might be a problem with the sharpener. For example the Pollux can be a little “fuck this pencil” and just break the point before you get to where you write with it. And a few times I have experienced that KUM blades after a lot of use are worn down to a place where they mess up the point in a way where it just breaks at the same point.
When I see the point breaking a lot. I always try with a different pencil first. Ideally of the same type. And if that also breaks I try with a different kind of pencil. If all of them break I find a different sharpener.
My go to pencil sharpener when I’m at home is the Classroom Friendly. One of the main reasons for it is that I very rarely have any problems with it sharpening anything.