YAY!! Steve, you were right -- and on your first suggestion! My drivers and bios were all outdated, from 2012! And there were some new updates available!
I first updated the bios, but that didn't solve the problem. Next...
Second, I downloaded the latest chipset driver, but I found out I already had the latest installed. Next...
Third, I installed the AI Suite II software, which launches and operates various motherboard utilities at startup (found under 'Windows 8.1 64bit' on Asus' Sabertooth p67 drivers page. This was the newest, so I decided to try it. I run Windows 10 Pro 64-bit). And this fixed it! I was so elated but remained skeptical, so I did a second trial, waiting longer (2 hours) before waking from sleep. Voila! Sleep mode indeed is working as intended!
Thank you so much, Steve! I really wanted to use this feature to save power! In closing, it seems plausible that there was a Windows update that rendered my drivers a nuisance to the sleep function.
Also, a separate point, in case it helps anyone: I noticed a few weeks ago when I enabled hibernate mode in Windows 10, start up became unbearably slow: a full minute before Windows login (first world problems, I know) when it usually takes 20 seconds. So, I disabled hibernate, and suddenly my startup time was fast like before. Just putting that observation out there.
I'll update here if the sleep problem resurfaces.
Cheers and take care!