I think this depends on whether the "spirit" of an AI representation is independent of the hardware it runs on. The human brain for examples is not independent of it's hardware. Our state of mind is represented by billions of neurons connected with each other. Thus, if our body is destroyed, we die. We could create a clone, but it would be another instance of ourself.
However, if a body (e.g. a robot skeleton) is just a hull of a consciousness, then we can't apply the definition of immortality as stated in the article. Because although each instance of the consciousness would have a limited lifespan, the consciousness itself becomes immortal. The best example for this is the AI Lobsang, a reincarnated Tibetan motorcycle repairman, in the Long Earth novel series written by Terry Pratchett and Stephen Baxter.
If we have an AI with the full degree of interconnective complexity of a human, and we want a real-time streaming backup(or 100 of them in many places for protection via diversity) - are we making a population of AI's that will instantly diverge from the original AI so they will initiate a new different AI, or are we making a high density media copy, each of which can be used to restore into memory as the original AI to start to 'live' as we power up? The copy might be 10 years separated in time from the deathof the original AI - unless it is not dead at all, and we now have 'n' of them, each with the same streaming backup. All running at 10 to ?? Ghz?
Things will get crowded indeed...
Backup tapes for a artificial general intelligence with "That is not dead which can eternal lie, / And with strange aeons even death may die." printed on them