How to keep fresh-made soft pretzels from getting soggy or stale?

Unfortunately you're fighting bread-physics... Bread with a high crust:crumb ratio become stale faster than those with low crust:crumb ratios like large boules or miches. Their large surface area allows moisture to evaporate quickly and the starches dry up and harden. This is why thin breads like baguettes are traditionally "daily" breads, i.e. made/purchased to be consumed that day. Soft pretzels have an even higher crust:crumb ratio than baguettes.

Breads with extremely high crust:crumb ratios like hard pretzels, crackers, and hardtack are usually cooked to the point of being dry to prolong their storage capacity. These bread actually "stale" in the opposite direction by becoming more moist.

There are a couple of things you could try that might help a little. It might take a lot of experimenting to get something that helps, and you will likely still need to reheat the pretzels just prior to serving them to have the soft texture you're looking for. Without re-baking or light toasting there really isn't a way to bring back the original crust texture.

• Use pre-ferments to increase the concentration of a-amylase in your pretzels. Using a prolonged autolyse and/or sourdough starter can increase the amount of a-amylase in your bread which has been shown to slow staling.

• Incorporate conditioning ingredients like fat, sugar, malt, or honey into your dough. All of these slow staling.

• Try baking the pretzels at a lower temperature. The article linked above also mentioned that higher temperature baking leads to faster staling.

For storage, your best option is probably to allow them to cool completely (15-30 minutes) then place them in a sealed container at room temperature. Placing them in a sealed container before they are cool fills the container with humidity, which then coalesces and makes the crust soggy.

Since Pretzels are a German baking good and many primary school children get Pretzels in a lunch box, especially German moms wonder again and again how to keep their Pretzels fresh. Many German cooking forums / threads say (and the commentators SAJ14SAJ and derobert here already pointed out)

1. Don't put salt on the Pretzel or remove the salt. That makes the Pretzels soggy.
2. Wrap the Pretzels in a dish cloth and put them in a plastic container or put them directly in a paper bag - in both cases store the Pretzels a cool place.
3. There is no way to have "fresh" Pretzels the next day without baking them again for a short time (after wetting the Pretzel a bit).

Supposedly the lye makes Pretzels hygroscopic.

Somebody in the chefkoch-forum says that he/she wraps every single Pretzel in aluminium foil and puts them into the freezer. 2,5 - 3 hours before eating the Pretzels are taken out to thaw. The Pretzels are supposed to be ready to eat without beaking them again. I couldn't find this advice in other websites, so I doubt that this will work. But why don't try it? :)

Addendum: Maybe it is possible to re-heat Pretzels in a microwave for 10-30 seconds at 850W.

I've had soggy and I've had stale. A french baker once recommended to me that her baked goods should be wrapped in two paper bags and at best that should keep them for one additional day after they were baked. Since the majority of the time spent making pretzels is waiting for the dough to rise, for my next pretzel batch, I'm going to make the dough the night before, refrigerate it, and then bake the following day.

Freezing, wetting, and reheating may work. If you've ever had Super Pretzels sold at the grocery store, the pretzels come frozen and unsalted. The directions have you moisten the pretzels, add the salt, and reheat in the microwave. These steps seem to be all of the aforementioned techniques combined into one process. Perhaps homemade pretzels can be frozen and reheated in much the same fashion for times when fresh out of the oven isn't an option. I imagine a nice, firm crust achieved with sodium hydroxide holds up much better than the sodium bicarbonate approach.

I have made soft pretzels at home to give out as Christmas gifts. I made and baked them then froze them almost as soon as they were cool to the touch. It's been a awhile (7-10 years) but I think I dipped them in a baking soda mixture but did not salt them prior to baking. We reheated them in the microwave just like the store bought frozen pretzels, with 1 exception. Sometimes instead of water Id spread butter on them and then sprinkle with cinnamon and sugar instead of salt. They were quite good. Though you had to play with the microwave setting a bit to get the best result.