Yes, you can refrigerate most types of pancake batter.
The type of pancake that is not ideal to refrigerate for an extended time (more than one day) is a pancake with bananas, baking soda, or egg whites.
There are various reasons, such as becoming rotten or losing all the rise.
However, refrigerating any pancake for an extended period, over one day, will reduce the rise and keep the pancake flat when you cook it. This will be your most significant concern.
If you are OK with this, you can refrigerate your pancake for up to 4 days, but if you didn’t store it correctly, it would likely last a few days or hours.