It probably depends on what's actually in your shake. After all, there are commercially prepared versions that sit for months in the store. But they're homogenized and sterilized. Home-made concoctions are probably best used soon after mixing.
If it includes creatine, that won't last more than a few hours.
In general, shakes and smoothies are suspensions of small particles and air bubbles in liquid. If allowed to sit for a few hours, it's all going to separate, and loose any "body." Some of the ingredients will end up stuck to the bottom of the container. (Unless you have a high-pressure homogenizer available.)
Any fresh fruit ingredients will immediately start to oxidize and loose flavor and antioxidant properties.
As soon as you mix supplement powders with liquid, bacteria and mold will start growing in them. Refrigeration will slow, but won't stop this spoilage. As long as everything is cold when mixed and stays cold at all times, it ought to be good for a day or two.