Unless I'm missing something, all we know for sure is that they reached a point where to keep fighting Hammerfell was no longer worth it. Was that point when they had used up literally every soldier not crucial to their defense? Perhaps, but it could just as easily have been that they decided that Hammerfell wasn't important enough to spend more than X amount of their forces there. There are plenty of examples of wars in the real world where one side gave up, despite having the ability to continue.
Again, we don't know enough details to say for certain, so let's not act as if either interpretation is uncontested truth.