I'm looking for a word that encapsulates the phrases "freshness duration" or "duration until something is stale".
Shelf-life seems to fit the bill.
Definition of shelf life
the length of time for which an item remains usable, fit for consumption, or saleable:
the shelf life of fresh pasta
the new strategy will be lucky if it has a shelf life of more than a few months
In programming we use TTL, meaning time to live, on packets, cookies, etc.