added** The trick is not in the plug material but the cable plug sheath interface a.k.a. strain relief. Ideally it should be as stiff as the plug on exit and gradually be as flexible as the cable when it tapers off in about 20x cable diam. Very few consumer products meet this design spec and thats why they fail so often at the cable adapter interface. Its called impedance matching in transmission line theory and the same applies to electro-mechanical cables systems. Fix by solder is only temporary. **
Cables now use stranded wires twisted that are net the size of a human hair but slightly stronger like multi-filament fishing line, but nto that strong. ( read as > a.w.g. 40 strands)
THus they are extremely unreliable for rugged use. THis applies to all mouse cables near the mouse tail, thin USB cables at either end, all microphone cables near the wiggled or yanked end, power plugs & jacks AND headphone cable plugs and connections to headset. Note some USB plugs & cables are very robust.. Logitech's are NOT.
The fix is extreme delecate insulation strip, solder repair and heat shrink with any 15W iron 50/50 solder and heatshrink tubing, not electrical tape.
(Electronics parts stores sell heatshink tubing by cut lengths and it shrinks to 50% of original size.. Multiple layers adds durability so choose size accordingly. Ugly solutions include gob of PL-400 construction adhesive ( in pump tubes) around plug to wire exit for several inches (tapered) and allow to set once in a functional reliable position and allow to dry hard over a week. this may be durable stuff but ugly and extend life 25~50% depending on how bad it is.
Long term.. Look to adding your own heatshrink jackets to all 3.5 mm plugs in future at both plug and headset end. Most are poorly designed in China and do not account for the brittle nature of copper and many radial flexes and pull fatigue.
As a rule of thumb imagine the cable radius should not be smaller than 10x the wire thickness. For industrial ruggedness, consumers need to appreciate the flexibility of modern light thin cables but also their fragility. THat's why I add additional STRAIN RELEIF or stiff jacket material at any transition from rigid plug to flexible wire. THis supports a gradual change in bend radius and reduces copper fatigue enough to double the life. To make it last forever, consider adding spiral wrap to make it bulkier and eliminate copper fatigue and never yank the plug by the cable. Copper is not much stronger than hair in the same diameter.
Most cable jackets are flexible PVC. Durable cable jackets use polyurethane but are stiffer. Some may also be using UHV gun radiation hardened plastic for cables just as they do for automobile tires to make them durable. A 5 pound pull test tells me if there is any strain (techono-geek term for stretchyness) then the cable jacket is not protecting the copper wire inside from Stress. You want the jacket to resist stretch or flexibility more than the copper wire can withstand as copper is malleable but after a few flexes becomes brittle, which is why they went to smaller multiple strands, which then made it more sensitive to stretch fatigue.
Sorry only recommendation are inexpensive fatigue free clear sounding good bass "Smokin' buds" from SkullCandy.com with lifetime warranty avail at your local Radio Shack or equiv.