There is no such thing as a primer pin ....but I'm assuming you are talking about the "primer" itself in the base of the shell - that the firing pin in your shotgun strikes to fire the shell. ( just to make sure we're talking about the same thing here )...
But a 1 yr life is nonsense on any shell ....
If you store shells in a dry environment / they should last at least 20+ yrs with no issues. Eventually, the powder inside, may break down ....but it would be rare even after 20+ yrs.
I reload / so I have primers ....to be put into new shells as I reload ---for handguns and shotshells that are well over 5 yrs old on my storage shelf.
I recently bought 10,000 handgun primers from an old fella that was getting out of reloading / that he bought about 20 yrs ago and never used ...and he let me test a box of 100 and they were just fine. He assured me they were stored inside his home / dry / no humidity --- and the boxes showed no signs of any moisture or corrosion. I've since used them to reload 1,000 cartridges and have had no mis-fires... I would expect the same form shotshell primers.
Now if the shells get wet / in and out of a boat / left in a wet shed or a real humid environment / left in a wet hunting vest --- then all bets are off ---and I wouldn't keep them past 1 year if they showed any sign of corrosion.