had the same problem i'd see what the code reads at auto zone. and go from there heres what i did.
i replaced map sensor. thermostat. and cleaned the o2 sensor. but i had warrenty and i did not kno this at the time. u better see if u have powertreain warrenty and take it in.
also 1 of my vacuum lines came off on the top of the engine and if it gets cloged it shut off. it started right back up tho
http://www.aveoforum.com/forum/f82/car-sputters-10891/
^^^^click there