I haven't worn my fossil watch (FS 4337 model) for some time & decide to wear it & shook it, adjust it, & it dosn't work. Usually when I don't wear it for about 2 weeks, I shake it & adjust it, it works.

If you have a Fossil FS4337 Chronograph, shaking the watch shouldn't be doing anything other than exercising your muscles; the movement is a battery-driven quartz movement whose movement is controlled only by whether the stem has been pulled out (stopping the movement and saving power) or whether the battery still has enough power to activate the stepping motors that move the watch hands. Based on the symptoms that you've described, I would suggest that it's probably time to change your watch battery.

Often, when a watch battery is running low but isn't completely dead, pulling the stem into time-setting mode will stop the movement and permit the battery to "rest," giving it (briefly) a bit more reserve amperage to put out when you push the stem back in. That's how you can sometimes get a quartz watch to run for a few minutes after the battery appears to be dead. That may also be why your watch has started running again after you've set the time and date.

Fossil analog quartz watches tend to use silver oxide (usually #377 or #379) batteries instead of longer-lasting lithium batteries. In ordinary use, I would expect a silver oxide battery to provide between 1 and 2 years of service before it needs to be replaced. I can't remember if Fossil chronographs (which also use quartz movements) use a silver oxide or lithium battery. Lithium batteries often provide an additional year or two of service in analog watches, compared to silver oxide cells; digital watches using them supposedly may last as long as 10 years with a lithium battery, assuming you don't use the backlight or audible alarm functions. Note, however, that these batteries are different sizes and different voltages, so you can't substitute one for the other.

Finally, none of this advice applies if you have a Fossil watch with a true mechanical movement in it. In that case, gently shaking the watch may spin the winding rotor enough to start the watch back up again. However, an even faster way of winding those watches is to use the winding / time set crown to wind the mainspring directly instead of relying on the geared-down action of the winding rotor. Automatic watches can bind up if they are not used for a period of time; the lubricating oil used in some of the pivots can harden--or at least provide enough resistance that the movement may require more initial force to start running than to continue running. That behavior usually indicates that it's time to have the mechanical movement cleaned and re-lubricated.