I had this issue once with NW and DL. I had booked a mid-morning NW flight ATL-MEM-ORD (connecting to AI for ORD-BOM), but was unable to make that flight due to a meeting that ran late. I tried to standby for a later flight, but nothing would get me there in time. While I was there, the computer actually cancelled my itinerary for being a no-show.
I went over to DL and bought myself a full-fare one-way ATL-ORD ticket and made my ORD-BOM connection on AI in the nick of time. At BOM, I went over to the NW counter and explained the situation - showing them my DL boarding pass. They immediately reinstated the itinerary.