As long as the re-termination is done right and with adequate strain relief, the connection will last. Factory termination can fail, which is the case here.
With your phones, you need to find 'where' in the cable the connection has failed. If it's at the plug end, the fix is as simple as re-terminating it. If it's at the phone/earbud end, it gets more complex and a full re-cable is typically what people do to fix it.