Leave it on the shelf and never play it works the best. Otherwise, expect this to happen because wood will always give when coming in contact with wood/other hard surfaces. Playing kendama will almost always ensure chipping somewhere on the setup, just keep jamming. Like @htimSxelA says, "Destroy All Damas"
Out of curiosity what brand tama is that? It looks like the grain on your tama is running horizontally. Many companies that make tamas usually run the grain vertically so that it won't wear like the one pictured. The tama pictured is probably a stall monster, but unfortunately I don't think that there is anything you can do to prevent it from happening.
I'm sure @htimSxelA can elaborate more on this, but i know that depending on which way the grain of certain woods goes will make it tear off like that much easier than others, though as he would also say destroy all damas...
Yea, poor design, not much is going to stop that, except some proper product testing before releasing new products. I mean, maybe you could super glue the crap outta it, but I don't think that's a 'good' fix. You should see the purpleheart side grain test tama I have! It lasted like a week and looks much worse than this haha.