Parallels should simply come clean and let everyone know that they don't currently support Parallels Desktop when the host sleeps while on battery.
I am as frustrated as you are, and I think I should ask Parallels to compensate me for all the time I wasted troubleshooting on their behalf.
Since Jan 8, I had three remote sessions, sent multiple problem reports, tested different Startup and Shutdown options, reset ACL permissions, reinstalled Parallels Desktop 10 multiple times, reinstalled Parallels tools in the virtual machine, installed Trial version of Parallels Desktop 11, tested on a newly created VM linked to my existing HDD file, etc.. The problem was escalated to Tier Two that asked for further tests and logs. Their final response is "Our Developers ... are working to address [the issue] in one of the future builds of Parallels Desktop for Mac". (see below)
Note: About 2 months ago I bought Parallels Desktop 11 for my wife's Mac. Interestingly, waking from sleep works fine on her machine. The main difference between our two Macs is she's currently running Mac OS 9. But I was also running Mac OS 9 when I first noticed the wake-from-sleep problem on my Mac about 18 moths ago.
Finally, I've recently installed the trail version of VMWare Fusions 8.1.0 on my Mac and I've not experienced any problem waking from sleep. I'm doing some informal performance testing, and with it I'm finding VM startup times and application launch times are in the same ballpark as Parallels. I'm really tempted to switch to VMWare where a single license will cover both our Macs. However, my wife has just gotten used to the Parallels UI model, and I don't want to confuse her with VMWare's slightly different UI model at the present moment.
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Final Response from Parellels Tier Two Support
-----Original Message-----
From: Anzhelika Khapaknysh, Parallels [mailto:support@support.parallels.com]
Sent: Tuesday, January 19, 2016 8:33 AM
Subject: [Parallels #2224361] Wake up Mac from Sleep when Parallels is running
Gene,
Thank you so much for all provided details and logs.
Our Developers are already aware on the issue you reported and they are working to address it in one of the future builds of Parallels Desktop for Mac.
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