Keep in mind that whenever you roll dice - be it one or more - for a given purpose (to determine damage, if an attack hits, or if you shake off a save-ends effect) it's considered a roll. Bonus dice for a roll, such as those granted by the Hunter's Quarry or Warlock's Curse features are considered part of that roll.
So, the Iron Armbands of Power only grant their bonus to a damage roll once, not once for each die rolled. Also, notice that the Armbands only provide this bonus to melee attacks. That is attacks that have a range indication of Melee. They do NOT confer the bonus to Close burst or Close blast attacks, even if those only have a range of 1 or are performed with a melee weapon.