Though I'd add that it also matters how many apps your running. Even with the 2A charger, I suspect you can pile on enough apps to drain the battery (since using the MHL cable (without an HDMI) charges, but when you start mirroring the screen it starts eating battery power)
That being said, my device checks like 5 different emails, has an 'always on' connection to my desktop for iRemote, Talkatone (always-on VOIP) and often Skype, with screen on, and I dont have a problem, so... *shrug*