So a player has Stannis (" King, Lord Immune to location abilities. While Stannis Baratheon is the only King character in play, he gains vigilant, renown, and stealth") in play along with another character with a Banner Bearer attached (Challenges: Kneel Banner Bearer to choose a Knight or Lord character you control. Attached character gains all keywords the chosen character has until the end of the phase)

Stannis is then blanked via nightmares, does the banner bearer character keep the gained keywords?

Short answer, yes. Long answer: the keywords are determined at the time the effect is resolved and are not checked again.