Abraham is not tired yet. In Genesis 18:29 he descends one rung further in his negotiation, and the Targum spells out the logic most translations hide.
"Perhaps there may be forty found there; ten for each city of the four cities, and Zoar, whose guilt is lighter, forgive thou for Thy mercy's sake."
Notice what the Targum adds that the Hebrew does not: Zoar's guilt is lighter. The rabbis preserved a tradition that Zoar (also called Bela) was the youngest of the five plain-cities and had not sunk to the full depravity of Sedom and Amorah. That is why, a chapter later, Zoar will be the only one of the five to be spared at Lot's request (Genesis 19:21).
Abraham, the Targum is showing us, is not simply negotiating a number. He is making a moral distinction between the cities. He is asking God to grade them on a curve — to weigh the four worst against the one that is merely bad, and to let mercy cover the difference.
And God answers: "I will not make an end for the sake of the forty innocent ones."
There is something quietly magnificent in this. Abraham is teaching prayer itself how to work. You do not petition Heaven in generalities. You name the precise injustice you are afraid of, you name the merit you are banking on, and you ask for the specific shortfall to be covered.
The takeaway: mercy, in Jewish prayer, is never cheap. It is itemized.