Jim Hague said:
Like I said - it's not the 'smiting of evil', it's the fact that the paladin:
1) Killed a helpless opponent (thereby losing any justification in the LG alignment property of 'mercy').
2) Has a pattern of this behavior and has committed similar acts in the past, according to the DM.
We're here debating about the Paladin losing his powers. They can be lost three way:
1) Gross violation of the Code
2) Committing an Evil act
3) Ceasing to be Lawful Good
I can now summarize why the Paladins actions were not any of those three (without using straw men, I hope, but RAW):
1) The code is silent on mercy, but calls for punishing those who harm innocents. The Paladin punished a Halfling he had ascertained to be 'in' on the attack. So he complied with his code (which still is silent on mercy, BTW

) Check.
2) He meted out some Paladin-type punishment on a creature engaging in evil activity. Punishing evil is not evil. Hence it was not an evil act. Check.
3) Not showing mercy might not be a [Good] action, but it isn't [Evil] either. I direct you to PHB alignment section which states that Alhandra the LG Paladin fights evil 'without mercy'. Check. EDIT: Just to make my case fool-proof: one neutral act doesn't shift your alignment from Lawful Good.
Because those are the conditions you loose your P0WRZ with, and none of them were fulfilled, it stands that the Paladin keeps his P0WRZ. We cool, Jim?