Even if mix is poor, I struggle to believe that the GRU/EZE route is not extremely profitable for BA at the moment, as its fares are so high compared to its other routes and also to other airlines to Latin America.
For example, from London, even off-peak the lowest BA economy return fare to GRU is £720 (£800 to EZE), and there are absolutely never any promotional offers. To the west coast of the US, roughly the same distance, in winter you can fly for about £300 return.
BA's business class fares are also much higher than any other airline operating Europe-Latin America flights. For example, from LON to EZE return, the minimum return fares I can find are:
BA - £2600
Iberia - £2000
Air France - £2100
Aerolineas Argentinas - £1600
Lufthansa - £1700
Despite BA's high fares, CAA stats show that the planes are full. High load factors and high fares together implies that demand is not being adequately served at the moment - and so there should be a gap in the market for TAM, and perhaps a second UK carrier, to fill.