@sozobe,
I clean mine with a very diluted amount of clorox and water. Rinse and wring it out and keep it in a baggie. It will dry out and be hard as a rock if you don't keep it moist. Because we practice or play just about every day I am always cleaning it and rinsing it. I have never had a problem with mildew. In the off season I put it back in the plastic container it came in and let it dry out. It doesn't seem to bother it at all. I don't think it would hurt to wring it out really well and put it in an air tight baggie either.
When I pull it back out, I just run cool water in the container and pull it out and start all over again.
I am so glad she likes them. It really has been the best little find for us.