How do I keep bagels from going soft?

We have done this several times. We wait till the next day, slice them and freeze in freezer bags so we can see what we have.

I recently froze almost 300 bagels the day they were made. As soon as they were room temperature, I wrapped them all individually in aluminum foil. Even weeks later, they taste delicious when I pull them out of the freezer.

Your other question about how do crusty loaves stay crunchy on the outside is a tricky one. If you want to store your crunchy loaf in a container, I suggest glass or metal, as plastic tends to breathe in a way that lets in humidity. But that super crackly, crunchy crust will fade the longer it's not eaten. If I buy a levain loaf from a bakery and I can't eat it all the day its made, I pack it in a brown paper bag, but it won't be the same the next day, it's true.

Levain made breads do not stale/change quickly, because they have no "commercial yeast" in them. The more yeast that's in a bread, and the more humidity that is in your region, will add to the staling aka - soft/wet/less crunchy exterior of your loaf.

I freeze whatever I'm not going to eat immediately. I agree with HalfPint and Pierino, they go stake quickly.

With most baked goods, let them cool completely on a rack with good air circulation. They'll be fine for most of the day, but should be frozen or wrapped (or put in a container) by the end of the day. Breads and bagels are fresh and best the day they are made. After that, they can become stale. Edible but stale. So I often freeze and then reheat in a toaster oven directly from the freezer. Almost like it was fresh baked. Almost ;)