I'am not sure what your problem is.
If you renting at the parks you rent for what days you need. But remember once you reach the gate the wheelchair gets turned in. You have to walk to and from the bus and from the bus to your room. Also on busy days is first come first served.
If you need a wheelchair 24 7 you need to rent from an outside vendor preferably a authorized disney vendor. Which means the chair can be left with the bell captain before you arrive and left there to be picked up by the outside vendor. Also outside vendors are cheaper.
I been renting scooters from apple for years.