How to preserve an open box of dried yeast?

The main enemy of dried yeast is moisture. As long as the yeast remains dry, it remains dormant and preserved. Once it is exposed to moisture in the air, it will begin to absorb said moisture and the shelf life (even when stored at the recommended fridge temperatures of 2-4 degrees Celsius) will start to shift from that of dry yeast to that of liquid yeast. This is why dried yeast is supplied in barrier packaging which is either vacuum (Lallemand) or nitrogen-filled (Fermentis).

So whatever you do, keep your dried yeast as dry as possible. Airtight containers, tin foil rather than low density polyethylene sandwich, butcher or ziplock bags, and as little air in the package or container as possible will all help to extend the shelf life of your dried yeast.

That said, dried yeast is fairly hardy, and your yeast won't go off right away in any case but gradually lose viability over time. So if you have concerns about the viability of your yeast as a result of storage conditions and time, simply pitch a little more to compensate and you'll generally be fine.

Lallemand states:

...must be stored dry, below 4˚C (39˚F). Exposure to humidity and oxygen will affect the viability and vitality of the yeast. Do not use soft packs or sachets that appear to have lost their vacuum. Once a pack or sachet is open, use immediately for best results. If kept sealed (or re-sealed) under vacuum and stored under appropriate conditions, dry yeast can be used until the indicated expiration date, which is typically 2-3 years after manufacture.

So, basically just keep it cold, and put it in a container that will seal tightly with as-little-as-possible extra space for oxygen. And when using the yeast- make sure whatever you're scooping the dry out with is clean. Dry yeasts are pretty resilient, storing as above should be fine. With distilling you have slightly less concern about contamination, but realistically dry yeast carefully stored/sealed is unlikely to get some type of infection on its own.

I think vitality-over-time is the bigger issue. Around 1 year, you may need to incrementally increase the amount of yeast you pitch on each run as you'll lose some cells.