Painter's Servant and Chrome Mox

[DrewliusMaximus]

How exactly does Servant's ability interact with Chrome Mox?

If I have Servant out naming blue, and imprint a red card on Mox, will Mox check the color of the imprinted card only once, or will it stop producing blue mana if Servant is killed?

[cdr]

Chrome Mox 0
Artifact
Imprint -- When Chrome Mox enters the battlefield, you may exile a nonartifact, nonland card from your hand.
T: Add one mana of any of the exiled card's colors to your mana pool.

"T: Add one mana of any of the exiled card's colors to your mana pool."

Whatever color(s) the exiled card is when when the ability resolves.