LAN has flights to MEX from LIM and SCL, TAM has flights from Sao Paulo. The LIM flights seem to turn around in 90 minutes, but the GRU and SCL fly overnight both ways. That means they leave GRU/SCL in the evening, arrive in MEX early morning, and then wait all day before leaving MEX in evening for GRU or SCL.

However, that's two airframes, so I'm not sure why there should be more than three (incl the LIM flight).

And it also seems a fairly inefficient use of aircraft. Certainly the SCL flight used to be a day flight northbound, but clearly is night both ways now.