Possible Clues:

• Kind of racehorse for which going isn't suited?
• Guy about to make a comeback, a tenacious sort
• Annoyed exclamation raised about the old person hanging on
• What's brilliant about the old horse? It has stamina
• A river, on reflection, is a river
• Not a drop-out in the long run
• A horse that's better in the long run
• One with powers of endurance
• Person with endurance, doesn't fall away
• Perhaps guest's one with lasting qualities