Prior to the United merger with Continental, UA used to fly from Washington-Dulles (IAD) to EZE non-stop and CO flew a through-service from Newark (EWR) via Houston Bush Intercontinental (IAH) to EZE using a 767-200. After the merger, United discontinued its IAD-EZE flights in favor of making CO's former EWR through-service to EZE nonstop and it continued the IAH-EZE flights. United will now keep the daily IAH-EZE 767-300 service.
United cited "lack of demand" for the nonstop flights from the New York area to Buenos Aires. Indeed, Argentine government restrictions on Argentine citizens' access to U.S. dollars plus the reciprocity fee charged to Americans to travel to Argentina have both diminished demand for flights between the two countries pushing any routes of marginal profitability between the US and Argentina into the "red" and that is what might have happened with United's EWR service.
On the other hand, Delta flew from New York-JFK to EZE nonstop in the 2000's but dropped the route after a couple of years and Aerolineas Argentinas has been in and out of the route (mostly out) during the last decade. The only airline that has flown from the New York area to EZE non-stop with consistency is American so maybe there is only room for one carrier on this route.
Although American will once again be the only airline flying this route non-stop, Aerolineas Argentinas is rumored to be thinking of flying one of its newly-delivered A330's to New York starting in December in the wake of United's departure.
Sources: http://airlineroute.net/2013/07/13/ua-ewreze-sep13/ via Eric Trum
Aviacion News 18Jul13