"I hope you like Harry Potter references, because I made seven backups."
In the cloud, obviously.
Seriously though, the point is we tend to imagine an AI as some sort of human replica made of silicon and bits, which is reflected in the Turing Test.
The problem is that the single attribute of immortality (not in the strictest sense of the word, but close enough) would make any AI as inhuman as anything we can possibly imagine, except maybe for some obscure deity.
We wouldn't share the same needs, goals, priorities, heck we wouldn't even be competing for the same resources, with the possible exception of energy. And even if we did, the AI wouldn't even need to compete: it can just slow down in a corner and wait patiently until we finally go extinct.
Pretty much like a teenager.