I just purchased an invicta 14213. I see that you wind it by shaking in a circular motion. My question, is it normal for the watch to stop running when you're not wearing after a little bit of time?
That's normal. As with any mechanical watch, it will eventually stop after a certain amount of time if you don't wear it. With your Invicta, you also don't have to wind it by shaking it in a circular motion. You can wind the crown clockwise to power up the spring and it'll start ticking.
Technically that is not a 'wind up" watch. The term wind up applied to a watch you actually have to manually wind every day to keep running. Your grandfather likely owned one but they are still popular today.
What you have is called an "automatic" where the watch automatically winds itself from the motion of your body. Most likely the longest "power reserve" (the amount of time your watch will remain running WITHOUT the motion of your body) is typically about 40 hours. Any longer than that and you will need to restart it by shaking it.