It will run out eventually just like .30-06 and .303B. Only a couple really small countries still use 7.62x39 for their military and the big producers aren't producing surplus ammo for arms they don't use. Pretty much every AK using country has converted to 5.45x39mm and has been producing only that since the 80-90's. I don't think I've heard of surplus 7.62x39 made after the late 70's other than Norinco that went into the mid 90's. There are many millions, if not billions of rounds out there still but there is also a civilian market buying up millions of rounds a year. It'll dry up, just like every other type of surplus ammo has. Could be a year, could be 10, no one can say with total certainty.
Relatively inexpensive new manufacture 7.62x39 will remain available due to it's popularity in the civilian market but it is still several times more expensive than the surplus. The new stuff can run $.40-.50/round while the surplus can run $.16-.20/round.