Continuous power problem with Nest tstat

[Trifog13]

From top to bottom this Nest thermostat is installed correctly and properly. Double and triple checked. 
Yet every single day there is a problem with it. 
The most troublesome issue is the very low battery warning that regularly appears. 
I have a power connector hooked up to provide C wire power but this warning shows up anyways. 
Currently these are the readings from the Tstat: Equipment -

wiring  Y(P)-W-G-R 

Power info - Vin: 34.271V / lin. 385

PS: Y-385, YP-28, W-10

power connector: Detected 

power test: unable to test 

What needs to happen so this Nest can function properly?? 
Please, any assistance is greatly appreciated as little to no info is available online to troubleshoot this problem. 

[Trifog13]

Restarting the Tstat several times is usually my go-to method for fixing the problem. That method worked again tonight. 
Why does this keep happening?

[spinningbrian]

I have the same issue with frequent "very low power" messages despite hardwiring it for power and having good batteries. When I check the battery voltage in settings it reads the same as it does on my multimeter at >1.5V per battery.  Have you checked your battery settings too to see if they read about 3V (since there are 2 x 1.5 each). I haven't found a fix in my past searches, so trying the forum now.