Yeah, they had a big problem with starfish here in California. They sent teams of divers with knives to cut down the population. Instead the population exploded and made the problem even worse.
As the question is, I'd say that you could probably eternally propagate stem plants by cuttings. However, on a time scale that long I'm pretty sure your going to see changes in the lines of cuttings.
Example:
You have a stem plant and you take two cuttings.
You send one cutting to someone and they begin taking cuttings as the plant grows. We'll call this line of cuttings A.
You send one cutting to someone else and they begin taking cuttings as the plant grows. We'll call this line of cuttings B.
Over the time frame, Eternity, I would suspect you would see changes between line A and line B due to random genetic mutation. The mutation may not be through out the whole plant but it may be in the part you cut and therefore the cutting would contain the mutation. Remember, even though we are talking about asexual reproduction, no meiosis, there is still mitosis which is still susceptible to replication errors resulting in mutation.
This actually may be the limiting factor in propagation. We find now in numerous pet species that heavy breeding has resulted in shorter lifetimes due to genetic disorders; hamsters and rats get tumors and die much younger that wild specimens. The heavy breeding, or should I say inbreeding, is pretty much the same thing as you are reproducing tissue from the same dna instead of having an influx of fresh dna. There is also particle induced mutation possible as there radioactive particles everywhere.
So is it all the same plant? Yes, but it may not be the same plant it used to be. And, the limits to how many generation of clippings will be determined by luck, or chaos theory if you want to get all crazy about it.
Figure this one out and you'll be able to decide the ethical concerns of cloning.
Just my view on it
