Every time the lighting changes you need to rebalance the CWB. I carry a gray card in my larger camera bag and I pull it out and use it anytime I'm taking a photo where the white balance accuracy will matter (so if I'm just out having fun shooting, I don't pull out the gray card.)
You can use a gray card whether you shoot JPEG or RAW. The difference is that if you shoot JPEG, you shoot a gray frame with the reference card, then set the camera to CWB and tell it to use that gray frame as the reference frame. If you shoot RAW then just take a photo of the gray card and then proceed with the rest of your shooting (but do re-shoot the card if the lighting changes.) The camera won't do any adjustments when you shoot RAW... instead you'll set the white balance when you post-process the images on your computer. But when you do, you can set the white balance for your images by picking the frame with the gray card and applying that same white balance adjustment to every image that was shot in the same lighting.
Here's a fairly extensive video on using gray cards (sort of an infomercial for the Lastolite brand... the brand doesn't matter, all gray cards will work the same):
Using Calibration/Grey Cards « Lastolite School of Photography