There's an excellent
pamphlet from the Florida Bar Association on POA's. One section talks about what a bank would do if it refuses to accept a POA. (Sorry, it's not paginated; you will have to find it.)
Whether a bank could refuse a POA simply because it was not "durable" would depend on the facts and circumstances. For example. if the principal was still capable of executing a POA that contained the durable language, refusal of the non durable document might be reasonable. However, if the principal no longer had legal capacity to execute a POA, then a refusal probably would be deemed unreasonable.