Excuse the snark, but it's exactly as interesting as saying that some living systems are immortal until they're no longer immortal. If a protocell or a virus stops being alive (if we grant that it's alive) when it falls into a fire then it's not immortal just because it has no metabolism.
>Once started, their schedule (when they will deplete themselves, collapse, etc) is known and predictable, thus not alive.
Actually, no. For example, a star could hypothetically fall into another much larger than it and prolong its life, if we were to say that it lives. The only reason it's predictable is because a star can't move on its own to hunt weaker stars, and because (at least at this time in the history of the universe) stars are far enough apart that they rarely fall into each other. If that was a common occurrence it would be much more difficult to predict how long until a star burns out.