Have you tried the above out? Could you share some pics of the setup?

My issue was always with the Edimax wifi suddenly drawing too much power and rebooting the raspberry. A powered hub worked but it means my Rapiro will not be making any "long distance travelling"

So you got 2 problems actually.
1, A stable power source to the pi
The answer is pretty clear on the above chart.
So as the key issue is 'Rapiro board is not passing enough power to the pi', we need to feed power into the pi's micro-usb. That power should be DC 5V and so the easiest solution is to find a tiny DC-DC converter that you can put into Rapiro's head and connect its output to a micro-usb cable, then plug into the pi. The input to that converter should come from the DC input and battery box. I'll attach an image but as my Rapiro's head is crowded so it may not appears to be very clear.

2, A good battery to power it long.
So as I said again, use 18650. I'll attach an image too. Just modify the battery box slightly to house the batteries properly and you get about 4 hours with WIFI, occational camera and movement.

The batteries

Some explanation.

nice :) Thanks for the pics and cute pony.

Hi llacarte :
How do you change the betteries box into 2 18650 ?

Before i buy this, do you believe this will work?
https://www.amazon.com/gp/product/B00U2DGKOK/ref=ox_sc_act_title_1?ie=UTF8&psc=1&smid=A3CA5H83RV6W5M
Thanks!

Nice tip. just one question do you have a link of what product you buy for this only? "Connect the power source to a ‘7-12V to 5V’ converter"

Thank you

@coerrace and, sorry it is too late @mgudesblatart
Just happened to came back to the forum and found the question ;p.
I'm using this one.
https://www.amazon.co.jp/dp/B00KCYNEQG/ref=pe_492632_159100282_TE_item
I don't think you can buy this outside japan, but I think as long as it is a converter to output 5V preferably more than 2A from the source it should work.
Good luck!