It comes down to "what stays the same when all its atoms are replaced" and "how can we tell it is the same entity and not just an identical but different one". I think the answers are "shape" AND "continuity".

E.g. all "atoms" of a glider in Conway's Life get replaced every couple turns but an observer can tell it is still a glider because it keeps the shape, and it the same glider because it continues it's previous state.

This makes AI not quite alive because it's missing the continuity.