Hey, guys!
Im new here at wpcentral forums and I have lumia 1020 as well.
I bought it in the mid of october, after 1 week of the same problem you have - i went to shop and replaced it to another piece. Both samples had 3049.xxx.yyy(amber upd) firmware out of the box and both were discharging extremely fast--10%/hour even in flight mode(wtf???!!)
Later, it has been ota firmware update to 3050.xx.yyy.1002, then the battery life became a little more - 17~24 hours in standby...
I've noticed that after you full charge it and switch to flight mode for 1~2 hours and turn off it(flight mode i mean) later leads my standby up to 30~36 hours....
And if u start to use, it still drains f***ing abnormally fast, but better than before - damn i bought this smartphone not for putting it aside in standby mode? What the heck it is Nokia? Where r those battery lifes from E71/E72 haa...???!!!