Latitude e6410 powers on and off by itself

Hello,

I received this Dell e6410 second hand and it has worked splendidly for the last 6 months.  I have upgraded it to Windows 8.1. However about two weeks ago it has started doing the following:

Initially it would begin Sleeping by itself while using it, despite using the a power plan that did not allow it.  It would Sleep and then power off.  It was a sudden loss as the screen would dim as it was shutting down. It has now progressed to completely power down randomly.  When this happen the notebook will not power back on from the power button.  Instead I have to unplug the power source and battery and reinsert those and it will power back up no problem.

While this was obnoxious and did cause some lost work. It happened relatively intermittently.  

A week it has started powering by itself after send it a shut down command.  Sometimes it happens immediately sometimes after leaving it alone for hours.  To test this I would shut it down shortly before going to bed and the laptop would be powered on in the morning.

It became relatively unusuable as this power cycling would continuously happen.

To resolve this I have tried the following:

*running Dell Diagnostic utility (passed, even the full diagnostic)

*turning off automatic restarts

*checking the bios for wake-on situations (none)

*checking the Windows Event Log (nothing other than an Unexpected Shut Down)

*updating the bios (now up to a16)

*monitoring temperature of GPU/CPU (all normal, even under stress tests) 

*re installing the OS

All of those did not change the outcome however re-installing the OS made the computer usable again and seemed to fix it.  The power situation worked as expected.

Up until 4 days ago. It began the weird power cycling again.  This time with a vengeance.  Now it would shutdown and try to restart and it may not finish the POST every time before power cycling by itself again.  It may do this several times before it corrected, but only usually after I had pulled the battery and power and let it sit without power for several minutes.

I managed to reinstall the OS once more and it did power cycle again by itself upon the first couple of boots but it has now leveled off and seems to be working fine.

Any idea what is wrong or what else I can do?