NY-Buenos Aires is actually a pretty slim and fluctuating market that is more O&D in nature. Traditionally it never does that well for airlines. United could never make it work for more than a year or so at a time. Delta and American come and go, ramping up and down frequencies from one year (or month...) to the next. For connecting traffic it is too far north to be a convenient option for many destinations that are closer to Atlanta, Dallas/ Houston or Miami without cannibalising these connection heavy routes that traditionally always have done well as a result (and Miami for being Miami).
Aerolíneas, given that it is traditionally very Argentine focused, just doesn't have the presence in the US market to capture much connecting or inbound traffic especially when pitted against obvious choices like Delta and American. Also NYC as a destination for Argentines is the first to suffer in times of downturn as it is far more expensive than say Florida for the average tourist. As a destination It is a "prestige route" for them.
Personally I suspect that if they ever do privatize Aerolineas (more to the point, find a buyer willing to take on the black hole that it is...) it will scrap its long haul operations and funnel those pax through code-share arrangements with Delta, Air Europa and ITA while focusing on what it does better, serving domestic and regional markets at the bottom of the world.