Amazon prime generally users a courier, couriers on next day don't generally deliver saturday as a rule, its an extra.
just saying...
I had this problem with amazon prime when it snowed. I got my new mobo last year from the other side of the Pennines which were snow covered, and on a free postage from wherever, but amazon prime couldn't manage to deliver a gpu despite the amazon warehouses being on the less snow covered side of the country...