Still kind of difficult to understand what you are asking for.

Since 2003 until 2008 my wife and I have gone to EZE from MIA and back as D1, D2 and now as D3 (i don't work for AMR anymore), once or twice a year sometimes.

We were never, and I mean never left behind. You have to choose your travel time wisely. Do your research.

Also, it is impossible to know, how many seats will be open, after fuel, cargo, delays and weather considerations, until the day of.

I don't know about DEL, but AA you can have a pretty good idea on Jetnet a couple of days before the trip.

And always give yourself a day prior and a day after for Int'l. Specially to EZE and Santiago. Very heavy loads.

I hope it helps.