I've had this problem happen twice now and have 2 of the crystal copper braided Hifiman HE-500 cables that currently need to be rewired. Basically what happens is that one side of the cable (it connects it two separate small holes on both channels) always comes out of the pin that connects to the headphone. Is this something that can be fixed? I hate being without my headphones every time this happens since it takes Hifiman a week or two normally to send out a new cord. I'd be more than willing to pay someone for their time if this is a quick fix or something.
If the connectors are the ones in your March pics, you are twisting the body of the connector to put them on the headphone. The wires show evidence of being twisted. The fix is pretty easy but if you don't have a solder iron, you may want to take it to a Best Buy, Radio Shack, etc. and see if a bench tech will resolder them for you.