Actually it would probably prioritize self preservation over energy conservation, so it'd at least continue maintenance and, presuming it's smart, continuously identify and guard itself against potential problems. But even that will fail eventually, most likely some resource runs out that can't be substituted and interspatial mining requires more energy than it can figure out how to use or more time than it has left until irrecoverable malfunction.

In ultimate case, it figures out how to preserve itself indefinitely, but still eventually succombs to the heat death of the universe.