Powerbank and Samsung Galaxy S3 not working

I have a Galaxy S3 that has a very finicky USB charging port. I figured out that it would work with Monoprice cables reliably. I have a wall outlet with 3.4A combined capability with 2 ports. Charges fine there.

When I plug the phone + Monoprice cable into any number of decent powerbanks (Lepow, OXA, Xiomi) I have it either does nothing, or starts charging for a short time (seconds), then kicks out. The ONLY exception is 2 ENB powerbanks with 2x18650 batteries. It charges properly with the ENB.
(Note - had a couple cheap 1x18650 powerbanks that would charge for a short time, down to ~ 3.9v from full, then stop. I chucked them, why bother.)

Those same powerbanks work fine when charging a Kindle, Nexus, or Fire tablet.

2nd issue:
I also have 3 different USB meters. If I put those in line with the Samsung, doesn’t matter WHICH power source I use, it either does nothing, or kicks out immediately after a short attempt at charging, like seconds. Does this with the Wall power and ENB units also. Remove the USB meter > charging continues fine. This confused me for a good while as I was trying to use the USB meters to figure out what my charging problem was. Same USB meters work fine for other devices and a number of different cables.

Cables were a whole different problem. Took me awhile but I figured out there were cables that were completely lame, which often came with cheap Chinese devices, cables that worked but had poor throughput, and cables that simply WORKED. I’ve weeded the junk out and no longer bother with crap cables.

What is it that makes this phone so finicky? What is it about ENB powerbanks that works when nothing else will? Why do the USB meters not work for this phone?

I also have an Samsung Galaxy S3 (i9300) and my chargers, cables and USB meters work all fine.
Maybe some of your gear (cable, charger) is low quality, otherwise charging would work.

Investing in some good quality gear always helps avoiding such problems.
http://www.portablepowersupplies.co.uk/
http://volutz.com/micro-usb-cables/standard
https://www.anker.com/products/110/202/Micro-USB-Cables

https://www.tripplite.com/reversible-usb-charging-cable-up-down-angle-reversible-a-to-right-angle-5-pin-micro-b-black-3-feet~UR05C003UARB/
http://www.delock.de/produkte/G_84803/merkmale.html?setLanguage=en
https://www.sabrent.com/product-category/cables/2-0-a-male-to-micro-b/
https://www.tripplite.com/dedicated-reversible-usb-charging-cable-right-angle-reversible-a-to-right-angle-5-pin-micro-black-3-feet~UR05C003RARB/
https://www.tripplite.com/dedicated-reversible-usb-charging-cable-reversible-a-to-right-angle-5-pin-micro-b-black-3-feet~UR05C003RB/