If your solder points are breaking, it could be because their isn't adequate strain relief, or you're creating cold solder joints. To the first point, pulling on a cable should never put direct tension on solder joints. You could try wrapping a small zip tie around the cable on the part that stays inside the headphone casing, so that pulling on the cable puts pressure on the cable where the clamped zip tie contacts the headphone casing.

As for cold solder joints, you just have to make sure to properly tin the wire and solder point before connecting them. The solder point needs to be hot enough to make the solder adhere securely. Doing this over and over will probably start melting the plastic around the hot metal, so it's not great to solder and resolder a spot over and over.