I'm not seeing anything in your problem description which proves this is engine-related. You didn't mention any CEL/codes coming from this. If the engine were dropping out this much, one would expect that to be enough to trip the misfire counter.
Has anyone looking at your problem given any consideration to a transmission issue? There have been a number of transmission problem postings recently for 2009. Some of these problems have been found to be caused by coolant and transmission fluid mixing inside of the radiator/trans cooler. Has anyone taken a close look at the transmission fluid in your Aveo? (and the coolant as well). I'm certainly not saying this is your problem, but when multiple instances of the same issue show up on relatively young vehicles of the same year, it tends to send up the red flag.