No, we did not lose the rights. USA-Paraguay has Open Skies. Miami-Sao Paulo-Asuncion was flown daily until February 2006. The Paraguayan government set a new government-imposed travel agent tax which AA was not happy about. Given the marginal performance of the route, AA pulled out. American Airlines has guaranteed that they will resume service to Asuncion if the law is dropped. The proposing routing is Miami-Asuncion-Buenos Aires. It will allow AA to add a third daily flight to Buenos Aires, as well, because flights between EZE and a point not in the USA do not count towards AA's 28 USA-EZE flight limit, and AA has local traffic rights on ASU-EZE.
The schedule remains to be known. There is some debate on how exactly to schedule the flight.
A daylight in both directions would not require new aircraft. The 763 that is parked all day in EZE between flights to Dallas will simply turn around and do EZE-ASU-MIA during the day.
A daylight in one direction would have an overnight flight to Asuncion, and an evening arrival from Asuncion. This is the most likely canidate. It only requires one aircraft, and would allow good connectivity to major markets, such as NYC and Los Angeles. Until AA recently added the second daily flight to Bolivia, their Miami-Bolivia flights have operated like this since 1991, so there is no reason Miami-Paraguay, a similar demographic market, won't be able to work like this either.
A redeye in both directions is ideal, but would require the dedication of two additional 757s or 763s, which AA can't do.
It remains to be seen what will happen, but we first need to see Paraguay ease their government mandated travel agent commissions, which has caused a heavy reduction in air service to Asuncion (like the suspension of American and Varig) and scared off new entrants (like Copa).
