i am starting to have the same problem, where in order to get a charge to happen I need to apply a bit of pressure underneath the power cable such that there's a bit of an angle towards the front of the device for the connection to be made. If I don't hold it like this, it doesn't charge. This doesn't seem to be the case on *all* my cables, but since I have like 6 cables and it happens on several of them, I don't think it's a cable problem but the seating of the port. Someone else mentioned the different fits on different cables... i think the looser-fit designed-for-the-fire cables are the ones that are bad, but since cosmetically they don't look any different than the ones I had before, i can't be sure.
I think I'm going to call and talk to Amazon about it, as I'm also noticing the screen creep problem I had on my initial fire.