How would it know not to ask again if it can't store a cookie?

At least if this "Store cookies?" question is implicitly referencing EU regulations, those regulations don't require consent for cookies which are considered essential, including a cookie to store the response to the consent question (but certainly not advertising tracking cookies). So the respectful replacement for "Ask me again" is "Essential cookies only" (or some equivalent wording to "Essential" like "Required" or "Strictly necessary"). And yes, some sites do get this right.