I would love a nonstop LAX-EZE, I would be willing to pay at least a 20% premium for that and I would increase my frequency of travel. I suspect that I'm in the minority, as most people I know who travel that route don't do it that often. When they do, price is usually their main concern.
I believe AR used to have a direct LAX-EZE flight a few years back, nonstop on some days and with a stopover at LIM on others. I flew AR two months ago and the in-flight magazine had a dotted line listing future routes, LAX-EZE was one of them ("coming soon"). The website has no information about it, and I suspect it's been on the magazine for a long time.
I wonder what could be done to convince an airline to at least give the route a trial run for a few months. The flight would be shorter than the EZE-AKL nonstop already server by AR with an Airbus A340. Maybe even a 767 could do it.