Its not an issue of them not allowing you to book, its whether or not the room is available with the discount. There are only a certain number of discounted rooms available at any given resort, and when they're gone, they're gone. If they're reached their quota of discounted rooms for your travel dates (whether its
free dining or a discounted room) then the discounted room is no longer available. Free dining is nothing more than a discount
If you can't extend your free dining package try booking at the current discounted rate. Or you may have to change resorts for the extra night to get a deal.
You don't always have to change rooms with separate reservations in the same resort unless you're changing views (such as standard to preferred, or garden to water view)--you will need to mention it to the CM setting up the booking, and also discuss it with the front desk when you arrive so they can make a note. I've had three reservations at one resort... and never had to move, and that was on spring break when it was packed. You will have to check out of one reservation and check into the next, and have your room re-keyed. But it is entirely doable with little inconvenience.
Only time I've had to move is when they blocked my rooms for a large group. They offered to let me stay but I didn't want to be in with a high school band.