The short answer : Yes he does
To answer your question properly, we would have to know what Superman you are talking about. See As of 2012, how many different canon versions of the Superman character exist? for more details. If you are talking specifically about that Superman/Batman Apocalypse, then the question should be why does he keep his power, because he obviously does.
Anyway, I'm going to give you a few possibilities as to why Superman does keep his powers outside of our solar system. If you want more details, there are a lot of questions on this site about Superman’s powers.
First possibilities that come to my mind : Superman's powers come from a yellow star. Not particularly our sun, just a yellow one. And the range of a star is pretty good... The more bright is the star, the further its range would be. So even outside our solar system, either it is the Sun or another yellow star that gives him his power, Superman does keep them.
Second possibility : Superman's skin allow him to store energy. His skin stores the Sun's energy when it is exposed to its beams, and this energy can be used later. When there is no more energy, Superman loses his power. This is one of the answers to How did Doomsday killed Superman?