It isn't just another city
It was the capital
They could no longer send orders to troops
That isn't exactly how it works. When the head of command is killed, contrary to popular belief, those who were taking orders from it don't die. As a South American country I would not be surprised if the troops enacted guerrilla tactics and went on a low-risk defensive stance, mostly attacking entirely through ambushes and flanking. The battalions and whatnot in the other regions would become Autonomous for the most part, or go through some methods to link with one another and figure out another chain of command.
tl;dr Just cause you took the capitol doesn't mean that you automatically got half of Argentina. And after all, an autonomous force can be much more dangerous and ruthless than you or your men would expect if carelessly engaged.
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