With *A flying out of North America, your EZE choices are basically UA out of IAD and AC out of YYZ. AC doesn't fly to EZE every day, so you aren't talking about that many flights and they fill up quickly in Dec/January. People flying back to see family over the holidays plus other tourists tend to snap up the award tickets pretty readily. I'd actually expect EZE to be snapped up 10/11 months in advance. If you visit your family/in-laws, etc... every second Christmas, I'd start booking in February of the year before.

Suggestion might be fly to Brazil and then to EZE. More flights to Brazil with *A.