I went to a seminar by Wayne Carlton a few years back. He said store them in the fridge for the off season. I always for get and keep mine in my gear room with the rest of my crap. They last a couple years. I store them in the little carriers that they sometimes come in (like Primos ). I don't overthink it.
I try and save the little plastic baggy that they come in. And they usually stay in my pocket for a couple months after the season until I start using them again. I've never thought about putting them in the fridge, but they are usually in my truck along with my bugle, even in the "offseason".