Are you certain that there is no mechanical damage at the bottom of the affected bine? The symptoms you have sound like water stress, but if the other bines off of the same rhizome are ok then it is likely not related to root health. I would suspect something wrong near the soil line.
If there is no mechanical damage then to determine where the problem is occuring, you can take a knife and make a vertical slice (imagine you are whittling or carving the stem) into the vascular area of the plant, the cut should be around 1" long and go about 1/4-1/2" into the stem. Inside the cut, if you see green, then that section is healthy, but if you see brown then that part of the plant is dead. Make several cuts starting from the bottom, moving upwards to the top, and see if there is a difference in the stem.