Thanks for the report. My experience has been very similar. I think your evidence suggests that it isn't a power issue but a MS firmware issue. Annoyingly, my OP got stuck into this chain which is considered "Answered" so
I'm not sure MS people look at it again. This is very frustrating since I'm worried that this glitch like the one I posted about the problem with Daisy chaining Dell monitors won't get fixed.
My impression is that the Surface Pro 3 was released with great hardware but with fingers crossed --- not enough testing done maybe, because look at all the firmware fixes that were sent out to it working (really, the PC is an appliance with customized OS).
There have been 6 firmware updates since June, whereas most products get one or two at most during their entire service life (list from Microsoft site):
System Firmware Update – 9/9/2014
System Firmware Update – 8/19/2014
System Firmware Update – 8/12/2014
System Firmware Update – 7/16/2014
System Firmware Update – 7/8/2014
System Firmware Update – 6/19/2014
Given the 1-3 wk interval so far, maybe there's another coming for Oct. But these updates have got to slow down sometime as the various hardware get final adjustments. Could be we have to wait for Window 10. Some have tried the Technical Preview of it
(free download) on the Surface Pro 3 and say there are more hardware improvements. But it is an alpha test, possibly risky -- I think I will wait for the Windows 10 release in a few months.