It was a trick question. I admit. Well not a trick exactly, but a question to which science does not have a right answer. Even when the question is defined fairly exactly, it isn't clear what unit we should be looking at.
I've already talked a little bit about the hyrda, but I want to give you more detail, because they are such an interesting and bizarre case. There are at least four levels at which we could define the individual in hydra. The smallest is the individual cell. Most cells in a hydra are capable of turning into any kind of hydra cell, producing a whole new hydra, and moving on their own. People have turned a whole hydra body inside out, and the cells that were on the outside just become inside digestive cells, and the cells that were on the outside become skin cells, and the community of cells goes on about its business. Second, the polyp, that thing with the tentacles and digestive system we classically think of as the individual animal. It looks like a little animal. It acts like a little animal (in most ways). It hunts, it reproduces itself, it has different cells doing different jobs. Third, there is the physically attached cluster of hydra. Through budding (growing a new hydra-shaped organism off the side of the old one) hydra reproduce asexually, but the buds get to be a fair portion of the size of the parent before separating, and are generally of almost full complexity while still physically and physiologically attached. One or two or occasionally more buds can be growing off the main polyp at the same time, and one could easily see this mass of genetically identical connected cells as one individual, despite the fact that it has multiple sets of tentacles feeding multiple digestive systems. Finally, one could consider that these genetically identical groups of cells remain part of the same individual even after physical separation. The genetic individual could after a short time encompass many thousands of polyps.
At which of these four levels does senescence occur? We know from experimental evidence that the risk of death by individual cells increases with age, so we have senescence in level one. In level two, the polyp, the experimental evidence points to no senescence, and the same goes for level three. At level four we don't have experimental evidence, but Mueller's Ratchet implies that there would be slow senescence of the genetic individual. Without going into details, Mueller's Ratchet is a line of genetic reasoning which makes clear that the number of harmful mutations in an asexually producing population almost always increases with time, where the number could decrease with sexual reproduction. So as the genetic individual of the hydra keeps producing more polyps, the newer polyps on the average will always have more harmful mutations than those of earlier generations. And remember, just because the polpys don't age doesn't mean they are immortal. They still die, in large numbers, from causes such as being eaten. As the polyps are reproducing and dying, we end up with more polyps from more recent generations and fewer from older generations. The mutational load of the genetic individual increases, and over time this should lead to increased risk of the extinction of the genetic individual. So the genetic individuals, like the cells, senescence, but the two layers of organization in between, the polyps and the clusters, don't.
This is a real problem without a clear solution. Do hydra tell us something important about the evolution of aging, because unlike almost all other animals, they don't age, or are we just looking at the wrong scale?
A more useful way to phrase the question may be to ask why the cell and genetic individual age, but the polp and the cluster don't. The first answer that comes to mind is that both cells and genetic individuals accumulate damage in ways that they can't fully repair, while the polyp and the cluster can easily repair any damage that comes along because any one piece can completely rebuild the whole. In this context, aging occurs when organism are built in a way that doesn't allow for easy repair. At some point this idea will combine with some other idea to form something useful. Or it won't.