Hmm...4 day weekends every week...a whole continent to explore...sounds like you need to be marry an airline employee and fly free!
Seriously, sign up for the e-mail deals or visit the special sale fares sections of the major South American carriers. Definitely do this with Argentina's carrier, Aerolineas Argentinas, since you'll be based out of Buenos Aires (you lucky dog!). Check them as often as you can, and when you see a good sale for one of your weekends, by them! Airlines are always running good sales...you just have to check their sites at least on a weekly basis (or sign up to get their sales e-mailed to you, if they offer that).
Aero Continente
Domestic service within Peru.
http://www.aerocontinente.com.pe
Aerolineas Argentinas
The national airline of Argentina with international service within South America and to Europe, North America, and Oceana.
http://www.aerolineas.com.ar
Aeropostal
Based in Venezuela with service within the northern region of South America.
http://www.aeropostal.com
Aerovias Nacionales De Colombia S.A. (profile)
Aerovias Nacionales Avianca(AVIANCA). The Group's principal activity is the provision of international and domestic air transportation services for the carriage of passenger, freight and mail.
Grupo Taca
Providers of information and travel services for Grupo Taca (Transportes Aeros Centro Americanos), which is is comprised of 5 smaller airlines in Central America and services North, South, and Central America.
Guyana Airways
International network includes US, Canada, and points within the Caribbean; also provides domestic service within Guyana.
http://www.turq.com
LADE
Regional service within Argentina.
http://www.lade.com.ar
Ladeca
Domestic service within Chile.
http://www.ladeco.cl
Lan Airlines S.a. (profile)
Lan Chile SA(LAN). The Group's principal activities are the provision of passenger and air cargo services, commercial aviation services; operation and administration of customs enclosures and general-purpose warehouses; engaging in property inve...
LanChile
Chile's national airline with international service within South America and to North America, Europe and the Pacific.
http://www.lanchile.com
Linea Turistica Aereotuy
Provider of air travel to remote destinations in Venezuela.
http://www.tuy.com
Lloyd Aéreo Boliviano
Service within Bolivia.
http://www.labairlines.com
Pantanal Linhas Aereas
Pantanal Airlines provides regional service within southern Brazil.
http://www.pantanal-airlines.com.br
Pluna Uruguay
In conjuction with Varig, provides service within South America as well as to Madrid, Spain.
http://www.pluna.com.uy
Satena
Service within Colombia.
http://www.satena.com
Southern Winds (SW)
Regional service within South America.
http://www.sw.com.ar
TAF
Regional service within Brazil.
http://www.secrel.com.br
TAME Línea Aérea del Ecuador
Providers of information and travel services for TAME, which is is Ecuador's airline. Flights include the Galopogos Islands.
Varig Brasil Airlines
Brazil's major international carrier, with domestic as well as global service. English language website.
http://www.varig.com.br
Vasp
Mainly Brazilian domestic service.
http://www.vasp.com.br