A deal done with another neighbouring country or a faraway one (famous for its food after the pub) to supply some of the muscle to aid Argentina and get oil leases as a repayment is another way of looking at what could happen.
The neighbours probably couldn't muster much better equipment than Argentina at the moment, then there is the little problem of motivating other South Americans to go and give their lives for the Falklands. Personally I can't see China openly supporting a South American offensive and effectively taking on the rest of the civilised world.
An airborne assault? Four Typhoons and ground based anti-aircraft missile batteries could make an awful mess of transport aircraft positioning for a mass drop. A sea borne assault? - submarines.
How would Argentina neutralise these defences?