Thank you, yoganinja for sharing all your diligent work on the BSOD secondary to sleep!!!
My 11" Macbook Air Mid 2013 always reproduced the Black Screen of Death with Energy Savings set to default while running on the battery or power adapter following your steps:
shortened version: Immediately after screen turns black, tap any key or keys; keyboard lights stay on but device will not wake. Must perform hard boot to restart.
SMC P-RAM, EFI and SMC firmware updates produced "no joy".
Called Apple Support today and started a case number. The engineers got a Capture_Data.dmg file of the failure.
Dec 7th the tech called me and said the engineers want me to set up a disk partition to test my device to see if it is hardware or "software" (perhaps he meant "firmware"?) related. I said I really didn't want to do that and spend another hour on the phone. The tech said he will tell the engineers I "refused" and I said "whoa.....that's a little harsh, isn't it? Why can't they test this on their mid 2013 MacBook Airs? I've spent enough time on this--we showed them the problem and how to reproduce it." The tech said he would relay that info and for me to make sure auto updates are "on".
Meanwhile using the suggested "bandaid" and it seems to work:
apple/system preferences/energy saver/battery: 15 min and deselect box "put hard disks to sleep when possible/power adapter 25 min and deselect box "put hard disks to sleep when possible"
If others wish to create a case here is the URL: http://expresslane.apple.com
Now it sounds like I wait and see. At least they didn't deny a problem!
Case No. 538481151
MacBook Air 11" mid 2013, i5 processer/4gb RAM/256gb Storage
Noticed problem occurred after upgrade to Mavericks.