At work, I usually use my left USB port to charge my iPhone, while the right port connects to a hub on my monitor, providing Ethernet, external keyboard and sometimes another iOS device. I also have the monitor itself connected via one of the Thunderbolt ports. The computer is connected to the mains.
All of this works fine, but recently I've had some what I believe to be power-related issues with the ports. If I try to plug my iPad mini 2 into either port, it doesn't charge correctly (it keeps chiming to say it's charging, randomly, every second or so).
Another symptom appears to be that if I try to run Duet (the iOS/OS X app combo that allows you to run your iOS device as an external screen), it keeps trying to connect, the screens flash black, then come back, then keep coming and going but never connects properly to the iOS device. This is even the case if I'm using my iPhone, which doesn't usually have any problems charging.
I've tried removing all external devices and just plugging in the iPhone, and Duet still doesn't work properly. Same with the iPad and charging, if no other devices are connected, it still beeps all the time and doesn't charge properly.