I’ve heard that sneakers have a short shelf life. For example, you shouldn’t buy several of the same pairs because they have a short shelf life, you should buy new ones from current inventory as you need them.
Does anyone know why?
Maybe from a fashion pov, but I make each pair I have last about 7 years.
It matters with running shoes. The midsole will age-harden in a couple of years.
It’s because, as noted, the materials used in them will age. Some plastic and synthetics will harden. Some materials used to make soles in casual shoes will chemically degrade and literally crumble away. Leather needs maintenance so unless you’re planning to periodically clean/polish/moisturize them while they’re sitting in storage they’ll degrade over time, too.
With running shoes, which should be replaced every 500 miles if you’re a serious runner or athlete, you could probably get away with buying a couple pairs at once if you actually do replace them that often because you’ll use them before they degrade. But do you? Most people don’t.
I don’t know about sneakers, but I purchased a pair of Cervino hiking boots in the early 80s that were about 8 years old. The original owner found them to be a bit tight and wore them only once or twice. They were still in the original box and looked absolutely unworn. I wore them one winter for about two months, after which the sole snapped right in two across the instep. I stepped in puddle and the boot just filled up. There was no fix to it (other than a complete resole).
I don’t know about high-end running shoes, but I bought some budget Brooks running shoes at Big 5 over 20 years ago, and I liked them so much and the deal was so good that I bought three more pair. I’ve just about used up the third pair. I don’t do much running, and when I do run it’s either on grass or a treadmill, but I do quite a bit of walking in them on all kinds of surfaces.
Correct. People often fallaciously believe that if a product is professionally made in a factory from highly engineered and designed materials, it will just last in perpetuity forever (“factory sealed”) etc. But the materials do degrade. Leather will dry-rot. Plastic will change (sometimes turn yellow) even if it’s never used. So yeah, even if something is “new old stock”, it may still be unusable.
A lot of the plastic in sneakers and other shoes is (usually artificial) rubbers; while most of its polymerization happens when the pieces are formed, in the process called vulcanization, there will be additional polymerization just from time (not every rubber piece is vulcanized, but most are). This additional polymerization can make the rubber either harder and more fragile or softer and sticky; in either case, it ends up becoming unusable. The whole aging process is a big part of the design of rubber formulas and of the choice of which rubbers to use depending on how much life one wants to get and the working conditions: some rubber parts in cars are expected to last decades, others a couple of years tops.
A related question - what’s the best way to preserve running shoes? For example, if I bought 50 pairs of my favorite shoe, and took a pair out of storage every year, how should I store them? Some possibilities (all in a cool, dark place):
[ol]
[li]Vacuum sealed, e.g. using a food vacuum sealer[/li][li]In a low humidity chamber, either a desiccant or nitrogen storage system. Using a nitrogen chamber would also remove some O2, which could help.[/li][li]In a chamber under continuously pumped vacuum (10E-5 torr or lower) - this would also remove any outgassing elements from the shoe itself.[/li][li]Cryochamber, stored at liquid nitrogen temperatures, and continuously vacuum pumped[/li][/ol]
If money and effort are no objects, what’s the best way to preserve my favorite running shoe so I have a lifetime supply?
It would depend on the exact composition. Isn’t chemistry fun? 
But if you’re rich enough to afford 4, you can make a deal with the supplier to keep making you new pairs.