Look, I know Star Wars is junk science, but there is no need to make up more than needs be done.
It's made of gas and it was too big. That was actually the official answer when given by the JC at the Star Wars site (now sadly no longer in business) when this question was asked years ago.
The Death Star can't blow up EVERYTHING, obviously. It cannot blow up stars. It blows up planets. Gas gaints are a step larger than planets and are not solid. It's that simple.