This is what happened to us. I needed a ressie on day 8 of our trip. It wouldn't even give me the option from home.
When we arrived at our hotel, I was told that there was no availability on that day (we staged CL and even they couldn't help). Once we had been there for a day, the system would finally let me see the day that I wanted, but nothing was available for that day.

I kept checking and kept getting the "no availability" message. Finally, the day of, I logged in and several openings appeared. I grabbed one and we ate there with no issues. Thankfully it worked for us, but it doesn't seem fair that they would limit it to the first 7 days for guests who are staying longer than that.