Lifespan
... or around 6 hours.
Lifespan is an item property on certain objects that causes them to decay or disappear once the countdown timer has elapsed. Like the property Uses Remaining, lifespan allows the game developers to exercise a certain amount of control over the propogation of such items. Items with a lifespan generally do not enter the resale market.
The lifespan function of the Arcane Focus alerts the player to how much spell-time is remaining for his or her spellweaving character. In this instance, the lifespan attribute is more of an information source rather than an item restriction, though the gem will disappear when the time expires.