Hi BEA,
I've never heard of despegar.com, so I can't give you any advice there. However, I've always had luck getting cheap flights to Latin America at
www.exitotravel.com so you may want to check them out. Otherwise carefully combing through the internet is probably your best bet. I've also heard good things about
www.flycheapol.com although I've never used them personally. Good luck and send me an email if there's anything I can do to help you plan your trip to Argentina!
Happy Travels,
Lola