There's nothing in the 4e books that says a deity *can't* strip a Paladin's powers. But IMC it wouldn't even go that far. If the Paladin is not drawing on his Divine Power Source, he can't use any of his source Powers. If you want to Valiant Smite, you have to be Valiant, like it says on the fluff*. If you want to be a self serving coward, you better serve a deity of self-serving cowardice. And be a Blackguard. With different fluff.

This seems so obvious in the 4e system that it never comes up in play. I've never seen even a weaker player play a character at odds with the one described on his character sheet. The game
strongly propels you into playing the character you signed up to play. The thematics and crunch are so strongly mutually supportive that it's just never an issue at the table.
*Thing about 4e is,
you are roleplaying your character when you call upon your powers. Ergo:
Player: "I want to Valiant smite, but I reject Pelor and all he stands for, I am not being valiant, I am a snivelling coward."
GM: "Well then a Melee Basic Attack would be more appropriate..."