Hi nachowitz

Did you enable fast boot option in BIOS? I suggest try to disable it, also try disable hibernate is you set your PC as hibernate

Updating BIOS is necessary if you currently upgrade your Operating System, contact your PC manufactured for this process

Try to isolate HW issue by testing this machine at safemode. If PC still shutdown at safemode this will be HW issue

Please also check your HW, I suggest first run test for HDD

Recently my PC (Dell Optiplex 7010) has been shutting down without any warning on occasion, going to a power-off state in the blink of a moment.  

It requires a hard-restart (manually pressing the power-on button) to get it going again.

The only trace of a problem I can find is Event 109 in the event viewer - and this last shutdown was proceeded by 832 instances of that event logged in the five seconds from 8:11:09pm through 8:11:13pm.  

Similarly, copious event 109 entries were logged various other times this has happened.

At this point, I would estimate that it is happening a couple of times a week when I am in town.  

I have uploaded the event log here:
https://drive.google.com/file/d/0B6reMpcXOAM8aDR1cWwzVGtqU2c/view?usp=sharing

Can you please advise?

Thank you so much... So that I can understand, Is there anything in the event logs that indicates what the problem might be?  Why would disabling Fast Boot or Hibernate or updating the BIOS solve this problem?

The problem is new, as I"ve had this PC for 2 years.  I haven't changed configuration on any of these areas in many months.

Hi nachowitz

There is no detail information about what is the root causes of event ID 109, its only informed that your PC experiencing with shutdown

https://technet.microsoft.com/en-us/library/cc727090%28v=ws.10%29.aspx?f=255&MSPPError=-2147217396

Looking at event viewer, log files, dump files will isolate the issues which comes from OS and software side first. OEM PC like Dell supposed to be have diagnostic tools before windows login, also shutdown issue can be detected from light indicator. You can start the troubleshooting from SW/Windows first or HW first, depend on you.

I suspected this issue comes from HW or software conflict. If you are not experiencing restart or BSOD, high possibility this is HW issue

If recently you upgrade your OS from Windows 8 to Windows 8.1, BIOS update (maybe needed, depend on manufactured requirement) and driver (needed)

fast boot and hibernate is related to Mainboard, graphic card and power, disabling temporary will help determine if this issue caused by that specific HW. Some of OEM manufactured combine fast boot and build in software, that's also can be suspected as root caused

Other HW can be caused this issue is HDD, so I suggest you to isolate and test your HDD.

I suggest you also contact Dell for more details regarding HW troubleshooting

This information will be useful

http://www.dell.com/Support/Article/us/en/04/SLN285337