In the future, we will have gizmos and gadgets strapped to our wrists. But it doesn't make sense for everyone to have discrete watch circuitry and everyone have their own version of the correct time. In our connected future, everyone will get their time source from the same synchronized servers and we will all be on the same page. It is happening now.
If the wristwatch survives, it will be merely a connection to the internet, and the time will be generated from the internet. It will also provide GPS coordinates of the wearer and have some messaging built it. But I don't think that it is a likely scenario.
Take a look at the picture above. It comes from www.gizmowatch.com. It is a cellphone wristwatch. The time is provided by the cell phone function. We will see more and more of this integration of devices into other devices.
No, I am afraid the wristwatch will die. And we will never answer the question of why, when we want to get the time from a strangers, we point to our wrist, but when we ask for directions to the bathroom, we never point to the appropriate body part.