How long is ammo 108 good for?

There's shelf life and then there is SHELF LIFE. I'm still shooting stuff that was made before I was born. Probably isn't as accurate but if properly stored, ammo will likely outlive you. Some of the old WW-1 British 303 stuff still works with the occasional burp.

So long as the rounds aren't subjected to high heat or moisture, nothing is likely to happen. Most ammo manufacturers advise that their ammunition should be good for ten years

According to the DAU catalog, only Ammo 43 must be completed every four years.
That would imply all other certs (Ammo 67, Ammo 108 etc), do not expire.