There's a primer somewhere on here about making a frozen yeast bank. I'm not sure what all needs to be done but you have to prep it by adding it to another medium before freezing it to ensure the cells won't rupture and die.
Keep in mind that, after several generations, you will probably wind up with a different product. Unlike purchased yeast which is generally only a single yeast or, at most, a few yeasts, this will likely have bacterias, several types of wild yeast, and who knows what else. Something(s) will likely take over and dominate. But, most likely, after you get a starter up to a couple of liters, you'll likely have a dominate yeast anyway and it will be a non-issue.