My grandchildren have a couple of balls that sound like this and they've never gotten sticky. My granddaughter gives everything a bath including the ball and it is still OK. I'm guessing that the difference may be the type of material with which it's made. But the tags are long gone and so I don't know what they're made of. I'll check at the store and see what I can find out about them.
For the ball that has never been wet I think that probably static electricity is attracting the dirt and hair.
I also suspect that once it's gummed up and washing doesn't help it's best to throw it away.