Standards seem to counter the cumulative Fear effect very well. They don't seem to have much effect normally, a slight morale boost (probably capped?), but against Fear that boost seems to be added every turn, bringing morale back up toward normal.
Standards add one point of morale to every unit in an X square area every turn. If that would result in the unit reaching morale more than 5 points higher than they started with, the standard doesn't work.
So yes, in a combat with a fear-causing creature, the standard would probably continue to give a morale point a round for the whole battle.