I have both 2012 and 2013 Nexus 7, and can tell you with certainty that 2012 model has a very finicky micro-usb connection. A lot of the time even with original wall charger I find it not charging because it wasn't making a good contact. They fixed it in 2013 with a better connection.
So, I would do some troubleshooting first. Try to see if you can use Nexus 7 original usb cable (assuming you have no issues with it from original wall charger) and make sure it makes a good connection with a power port. Also, I'm sure you have a smartphone or know someone who has a smartphone and try to use your RAVPower ext battery to charge it up. If it fails with different usb cables and different devices connected to it, than something is wrong with a battery. Otherwise, it could be a problem with a loose micro-usb connection or maybe a bad usb cable.