I 'frequently' book EZE -LIM on LAN using BA miles but availability seems almost random. I found a flight a few days before Christmas but nothing in January in any cabin. Another problem I have encountered, and I have spoken to BA who don't have an answer, is flights can appear available on the BA website and you can book it all the way through to accepting your credit card. It then says the booking was unsuccessful. This has happened a number of times to me (only ever booking LAN flights through BA) and when I call BA they then tell me they see the flights but can't book them either.