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.