My Rolex that I have had for 9 years keeps stopping when I thake it off. I have to shake it for it to start again.

try winding by using the crown see how long it goes for it may be the bob weight is not working or as come loose

It seems to me that the company servicing your timepiece (Rolex or otherwise) must have missed something or did not properly service your timepiece.

You are correct that your watch should not require service every ten months. After servicing, your Rolex, like most all automatics, should run properly for 3-5 years depending on environmental conditions. Our Rolex service offers a one year warranty, and if any issues present within that time, the service is free.

I would recommend using a company that has a full time Certified Master Horologist on staff to service your timepiece that offers a warranty on their work. Thanks for the rating, and we are happy to help you and service your Rolex.

http://www.watchandpen.com/id76.html

Expert watch repair for Rolex Breitling Tag Heuer Movado

What's the question? From you description of the troubles you are having I suspect that your watch may on the outside look like a Rolex, but it certainly does not behave like one. I have never had such erratic behavior even with my much cheaper, but authentic Casios.

It's a very small timing gear, will roughly cost about 60.00 to fix it, has to be taken down part of the way to be put back into place, very common for them to pop loose

If you need further help, I’m available over the phone at https://www.6ya.com/expert/michael_2094e122cc46f24c

Nail on the head. Take it to a good repair/service shop that does Rolex service. Know this, it wont be cheap. But you will get the watch back in great condition and it will run perfect.

Your watch is self winding and will run down (if fully wound) for about 2 days.

This type of watch thrives on use and if not used will stop. To avoid having to re-wind by shaking, it should be worn every day.

(Some makers say that to full wind up their self winding watches, they need to be shaken (gently) aboiut 200 times).

Your Rolex sounds like it has a problem with the automatic winding gear train.A Rolex needs regular servicing when parts can be inspected and replaced.Servicing is about 3-5 year intervals.
You need a specialist Rolex watchmaker as only they can obtain Rolex parts.Try www.rolexrepairs.co.uk a full service will take 2-3 weeks.

If you haven't had it attended to since you bought it, then I suggest that it might need a clean.

Rolex will advise you if there is any other attention needed.

AS I'm sure you know, when changing the time (presumably by pulling out the winder), the watch stops.

Normally the watch re-starts when the winder is returned to the "in" position.

Check that the winder is fully home.

If it doesn't start, pull the winder out and in again. If necessary try this several times.

If this does not solve the problem, then a visit to Rolex may be necessary!

The advice given here is accurate to a degree. When wound, a rolex daytona IS running. However, it is the running seconds hand in the small sub-dial that is actually running. In the earlier Daytonas, this sub-dial was at the 9 o'clock position on the dial, (pre-2001 series daytonas). The later daytonas, from 2001 on, use the seconds at 6 position for counting seconds. The main sweeping second hand on the watch dial will NOT start until activated by the pusher at the 2 position. That pusher needs to be unscrewed and then pushed to start the large sweeping second hand. This action, in turn, starts the remaining 2 sub-dials in motion, counting minutes and hours. To stop the chronograph function, you push the pusher @ the 2 position again, to stop the sub-dial hands from counting, and then push the pusher @ the 4 position to re-set the dials to their "straight up position". This stops the chrono's function, until it is needed again, BUT the main running seconds, (at either the 9 or 6 sub-dial position, depending on the year series of the daytona) will continue to run, thus keeping accurate time.  Hope this gives you a better idea of how the timekeeping of the chronograph function on a Daytona works. So, to start your seconds running you need to start the chrono function by pressing the pusher at the 2 position. That will allow you to see the large sweeping second hand I think you're referring to here. Hope this has helped.
Doug