I have 2x Kathmandu power banks they have an output of 5V /1.5A capacity of 5200mAh 

The used to charge my iPhone 5S - but some time around August they stopped charging the iPhone. Its not the cable because the cable works fine attached to an adaptor or direct into a USB power point.  The powerbanks charger n non-Apple phones. The power bank also won't charge the iPad mini. 

Initially - a few secs the phone charges and then either it stops if I let it sleep   - or if I keep using the phone - I get a "this accessory might not be supported". From googling this seems to be a common issue. I need a power bank that will charge a iphone 5S - also I'd like something that will charge an iPhone 6s or 7s  as I may upgrade in a year or so . 

Its bloody annoying because they are just a battery -they provide enough amps - so why the heck should I have to buy an apple branded power bank.  Plus I can't actually find an apple power bank advertised in NZ - suggestions welcome