How long (minutes? hours? days?) can I keep a batter which is basically flour, oil, water and baking powder? I am concerned the baking powder will lose its fizz after being in solution for several hours. Or is it only heat activated?
Baking powder has 2 ingredients---one activated by liquid, the other by heat.
Pancake batter can be safely kept overnight in the fridge and you can cook them in the morning... they may even taste a little better. It will thicken a bit and may have some large "bubble holes" (I don't know what else to call them) but should be OK. The heat activated portion of the baking powder will kick in while cooking.
Longer than overnight, I can't really say.
Agree with iluvcookies, but want to suggest that since the ingredients are so few and simple, if time is an issue why not measure out and store the dry ingredients together and measure and store the wet ingredients together, separate from the dry ingredients, then combine them just before you need them. Storage/longevity will no longer be an issue but you've created a bit of convenience for yourself.
Any batter made with a leavening agent such as double (fast & slowing acting) baking powder, will initially have a leavening reaction when combined with the liquid in the recipe, causing the first pop of the batter, then lose it's leavening abilities if it is not used relatively quickly. After overnight storage, what you'll have left is a batter that only responds to heat activation, and you will not get the kind of rise associated with a successful baked product. Overnight storage will adversely affect cake batter, muffins, quick breads, etc. Pancakes don't need as much a rise, but it's nice to have light fluffy pancakes, which you will get if you have freshly made batter.
The fact that you don't have egg in your batter only exacerbates the rising problem, as egg provides not only ingredient binding, color, flavor, texture and richness but leavening, as well.
So, to sum it up, batters with leavening are better made to order.