Ive had the same problem with my z970. Actually i had the same problem with my first zte phone(z790) also..
With my current phone(z970) I find the problem. is complicated.. If i try a brand new charging cable, it charges fine for a while.. then after a few days or weeks, it wont charge anymore.. I have discovered recently that the outlets in my bedroom wont charge the phone at all, but everything else works fine on that outlet. I can charge it fine in the living room with the same cable.
I found a work around that keeps me functioning.. I have a small battery storage supply i bought on amazon for about $20. It charges my phone just fine.. So I just charge it up daily, and then charge my phone with it. I get about 3 charges from it, before it needs more juice.. This has worked fine for several months now.. I hope this helps you.. The Zte Z970 really is a great phone.. I have no idea why they seem to have charging trouble. Maybe they dont.. maybe we just got lucky?