Don't forget about this part of the rule:
Failure: If you attempted to intimidate the target during combat, you can’t try again against that target during this encounter.
I think the DM is well within rights to assign a moderate circumstance penalty per failure when attempting to Intimidate other targets, as well. "Well, Bob isn't afraid of the big bad dragonborn, maybe I shouldn't be either..."
-- 77IM
Failure: If you attempted to intimidate the target during combat, you can’t try again against that target during this encounter.
I think the DM is well within rights to assign a moderate circumstance penalty per failure when attempting to Intimidate other targets, as well. "Well, Bob isn't afraid of the big bad dragonborn, maybe I shouldn't be either..."
-- 77IM