I took the problem rose to the meeting last night. We has a special guest speaker: Paul G Olson and everyone agreed that although not overly obvious, this rose had a bad graft. If you closely, the dead piece was the actual graft. All the growth was from the root stock, not the actual graft.
FYI: Paul G Olson is a rose hybridizer and one of his more recent roses is Prairie Snowdrift. The presentation was excellent.