A lot of pathfinder ruling is about referencing all the way back as far as we can go, and then making a reasonable inference. Let's step through our logical process, bolding the important bits:
Abundant ammunition:
"When cast on a container such as a quiver or a pouch that contains nonmagical ammunition or shuriken (including masterwork ammunition or shuriken), at the start of each round this spell replaces any ammunition taken from the container the round before.The ammunition taken from the container the round before vanishes. If, after casting this spell, you cast a spell that enhances projectiles, such as align weapon or greater magic weapon, on the same container, all projectiles this spell conjures are affected by that spell."
So, we know that the ammunition lasts until at least one full round.
Smoke arrow:
"Arrow, Smoke: This arrow is actually a specially-shaped smokestick that can be fired from a bow. It trails smoke as it flies, and creates a 5-foot cube of smoke where it strikes. It otherwise functions like a normal arrow in terms of damage, range, and so on."
So, we know that smoke arrows are smokesticks that create a 5 foot cube of smoke and otherwise function like an arrow. Let's look in the smokestick rules.
"This alchemically treated wooden stick instantly creates thick, opaque smoke when burned. The smoke fills a 10-foot cube (treat the effect as a fog cloud spell, except that a moderate or stronger wind dissipates the smoke in 1 round). The stick is consumed after 1 round, and the smoke dissipates naturally after 1 minute.
Huh, turns out the ammunition is already consumed within a round anyway, but the smoke sticks around!
Now we have to make one assumption, and that is that:
the effects of abundant ammunition do not also disappear after one round, only the ammunition itself.
I think this is a reasonable assumption to make, if only because taking the opposite view creates all kinds of difficult situations where you have to adjudicate what is a 'permanent effect' and what is a 'temporary effect' (an injury is presumably permanent.. but what about a fire? A poisoned arrow?). This makes things much more complicated for little gain. Thus, using this logical flow and an appeal to simplicity at the end, we come to the conclusion that, yes, the smoke from smoke arrows duplicated via abundant ammunition should continue to last for up to 1 minute, even after the ammunition itself is gone (the arrow has burnt up already anyway!).
Caveat: if your GM has already decided that it doesn't last, he will probably challenge our assumption and ignore our appeal. In this case there's nothing that directly contradicts his interpretation, so you might just have to call him a prat and let it stand. If you believe it shouldn't last... well, I hope the flow of my argument has at least made you reconsider.