It's the salt.
Better storage strategy - store the ingredients and bake 'em as you need 'em - or make a batch each month.
Alternate to saltines for soups and such. Sailor Boy pilot bread. Long shelf life, tastes fine. No salt.
Sailor Boy does contain salt. It has about 45% less salt than the the Saltines (based on sodium content), but does contain salt. The recipes for pilot bread (aka hardtack) I am finding also contain quite a bit of salt. Nabisco Premium Saltine Cracker
INGREDIENTS: Enriched Flour (Wheat Flour, Niacin, Reduced Iron, Thiamin Mononitrate (Vitamin B1), Riboflavin (Vitamin B2), Folic Acid), Partially Hydrogenated Soybean Oil, Salt, High Fructose Corn Syrup, Yeast, Malted Barley Flour, Baking Soda, Vegetable Monoglycerides (Emulsifier), Calcium Carbonate. Sailor Boy Pilot Bread
INGREDIENTS: Enriched Flour (Wheat Flour, Niacin, Reduced Iron, Thiamine Mononitrate, Riboflavin, Folic Acid), Vegetable Shortening (Contains one or more of the following partially hydrogenated oils: soybean, canola, cottonseed), Sugar, Corn Syrup, Whey, Leavening (Sodium Bicarbonate, Monocalcium Phosphate, Ammonium Bicarbonate), Salt.
In theory, the monoglycerides in the Saltines should extend their shelf-life. It could also be that those crackers were a bad batch to start with, but we can't know that for sure if none were consumed shortly after purchase. Both products contain wheat flour, which can also go rancid. Even the malted barley flour could be the culprit. It may not be any one thing, but a combination of things breaking down. We can speculate all day on why (or even whether) one would go rancid and the other wouldn't, but without the equipment to test them, there really is no telling. Sure, there are examples of ages-old hardtack preserved in museums, but that doesn't mean they're still tasty.
_________________Feed science, not zombies
“People had more than they needed. We had no idea what was precious and what wasn't. We threw away things people kill each other for now.” ~Book of Eli