I noticed a similar issue on my iPhone 5 while trying to deal with a charging issue. Not sure if the two are related but I'm looking into it. The charging port takes a little jiggling to get the cord to charge. This is with the old original cord and also with the new one I recently bought. It doesn't charge well on the computer either, have to plug it in the wall. BUT as this was going on, I noticed some serious issues with my battery life depleting fast. It can sit off (well, sleeping) unplugged at 90-100% and then I'll get a text message 20 minutes later and the charge has dropped to 70%. I have no background apps running, have turned off data and wifi and haven't touched the phone. I've done a reset twice and upgraded the software. I haven't started doing anything new to the phone other than that but for some reason it just dies quickly with no use. I had the battery replaced in September as part of the recall of certain phones. I haven't been able to check my battery life status. They showed me a graph in the apple store when I went for the battery replacement but I'm at a loss of where they found that on the phone or how to find it myself. I've got an appointment at the genius bar for Saturday but if it's just a case of replacing the battery and charging port, I'll do it myself. I did it for the iPhone 3 years ago.
Thoughts? Anyone else have this trouble? I'd rather save the trip to the genius bar if it's just a dying battery and charging port issue.