[Keeper of Dol Guldur]

I don't know why it wasn't obvious to begin with, but I realized the last time I read (and remembered yesterday after watching Fellowship EE) that when Sam almost drowned in the final chapter, what went through Frodo's mind must have been very, very heavy. Both his mother and father drowned, and now his best friend was going to unless he did something. Pulling a sinking hobbit from a river isn't exactly easy for another, so maybe this explains a severe adrenaline kick just in the nick of time.