I could have sworn there was an official ruling on this, but I can't seem to find it. At any rate, Frodo can definitely use his ability to shrug off more damage than he would normally survive. When he was released, one of the preview articles mentioned using him to tank damage from Hummerhorns, which he obviously could not do if he were only able to cancel 1 damage at a time.
I think the effect is poorly worded (should be "When Frodo is assigned damage…"), but there is direct evidence of designer intent in this instance. Frodo takes any amount of damage, and then his ability wipes those hits away before he is killed (even though characters are supposed to die "immediately" upon taking damage equal to their health).
So, while a strict reading of the card text would support your position, and while I usually favor such literal interpretations, this is one case in which we do have an indication of official intent. Once per phase, Frodo can take any amount of damage as threat.