Micro USB cables are prone to going bad, so it wouldn't surprise me if you have several bad ones at once. Since you still have some that are fully working, I wouldn't think it's the port just yet. I'd stick with my usual suggestion of buying a new cable first. If that one gives you problems, then I would start leaning towards the port going out.
Another thing you can try is moving the plug about inside the phone, making sure to keep the cable as still as possible. If that causes the connection to come and go, it could be another sign of a bad port. Also try keeping the plug still inside the port, then bending the cable around right where it leaves the plug jacket (being careful not to actually kink it or go a full 90°, which could damage it during this test). This is the most common failure point of a cable. If the connection comes and goes this way, then there's your answer.