I have recently purchased a 2013 MBA 11" i5 4GB. I have this same issue. Sometimes suddenly goes to sleep after a few seconds, sometimes a few minutes. Frustrating, inconvenient and very embarrassing in front of clients.
This is on top of the widely reported wifi problems which I also experienced at home, where I had to change router encryption settings just to get an internet connection.
My first MBA (2011) had to be replaced twice due to completely dying after a few days (they suddenly wouldn't turn on). Then the final replacement had to have the wifi/bluetooth module replaced because it was dropping bluetooth connections. So much time in Genius Bars, and too much downtime.
My latest iPhone4 (bought after the last one was stolen) started overheating after 5 months. After a long drawn-out affair this was eventually replaced and within 2 months the replacement's silent mode switch is now malfunctioning.
Now I'm based in China, you honestly cannot get an appointment because the Genius bars are fully booked 24/7. Probably because their products are increasingly garbage. I'd have had this latest MBA returned ages ago but it was purchased in HK.