I agree with seoulmanjr. I also had a similar situation. I had booked award tickets through NW using NW miles and the itinerary was entirely on DL. DL had a schedule change that caused me to arrive at a connecting city after the connecting flight had departed.

I called NW, they rebooked me on an earlier flight. The problem was there were 5 of us traveling and we were in F. There were only 4 perksaver seats available on the earlier flight. I asked NW what they could do about that as it wasn't our fault that we had to change flights. They said not to worry, they would contact the partner desk at DL and get the 5th seat. Sure enough, they did and all was fine. Point being, this stuff probably happens more often than not and they can fix it pretty easily.