Yep, same here. Computer sleep is turned off (for power adapter, and I'm plugged in when this happens), and Put hard disks to sleep is also turned off. Display sleep is set to 10 min. I've had this problem ongoing for months. Over the past year, I bought new drives and a new USB hub, and I just upgraded to Mavericks. No change - still having the problem with both external drives, one of which is connected directly and one of which is connected through the hub.
In fact, after upgrading to Mavericks, now my external display ALSO becomes inactive upon waking. I have to unplug the display cable from the laptop and plug it back in for it to work.
This is ABSOLUTELY RIDICULOUS. And the fact that this drive problem has been occurring for this long with this many people is outrageous, especially since Apple no longer ships laptops with mechanical drives (which have much more storage), pretty much forcing you to use an external drive.
I've been a Mac/Apple fan for over about 25 years (even worked there for a year), and never have I seen so many problems than in the past couple years (not just talking about these issues - their entire cloud system is a mess among other things).