Let us remember that the rose in the novel appears at the beginning of the story, and Dr. Heidegger pulls it out as a dried, withered rose that was given to him by his fiancee before her untimely death. Although we could therefore say it was a symbol of regret, sadness and guilt, actually the way in which the rose is used to "prove" the efficacy of the water and it rejuvenating effects, results in a more important overarching symbolism. The withering of the rose signals the fate of the old friends of Dr. Heidegger and the temporary nature of their rejuvenation. Yet note what Dr. Heidegger says about the rose once it has withered again:
"I love it as well thus as in its dewy freshness," observed he, pressing the withered rose to his withered lips. While he spoke, the butterfly fluttered down from the doctor's snowy head, and fell upon the floor.
The rose is therefore a symbol of the central lesson of this allegory: we must not despise old age but must try to see it as another important stage of our lives to be cherished. Just as Dr. Heidegger has learnt to value the increased wisdom and experience he has gained through going old, so he has learned to love the withered rose just as much as he loved it in his youth. This is the lesson of the story that his guests fail to learn: old age has its benefits as well.