I use this brush to start almost every landscape I paint. It's called a hake brush and it's used to lay down large areas of color. It sees a lot of water and over the years that has caused the wood in the handle to expand and contract which has split the paint and caused it to flake off. I haven't soaked it in water, stored it bristles up or left the handle wet, but occasionally the handle does get wet though normal use.
I should have done this years ago, but I finally decided to repaint the part of the handle where the damage is. Hopefully this will help. It can't hurt.
