Car needs to be picked up by end of month?

I just put a deposit down on a preowned car from a dealership and it's in the process of being certified. The rep asked us when we could pick it up and we said the first weekend in October. He said it needs to be picked up by the 30th because cars can't roll over month to month.

I feel like this is a tactic to sell the car before EOQ. While we could technically pick the car up on the 29th, it means we have to cut a planned vacation weekend short and rush out of town to drive 3 hours.

Has anyone heard of this before? Should I push for concessions to pick up the car on their timeline?