RUT955 does not have "Sleep mode" functionality, therefore it cannot be shutdown/powered off from software side. I.e. If you would connect voltage to the router, router will be powered on as long as this voltage is maintained. Triggering router's inputs would have no effect (would not turn the router off)
For such solution you would need to use additional external device - relay with timer, so that relay could still be active (and power on the router) for certain amount of time after ignition is lost.