I have had no battery issues at all with mine...

I was under the impression that the 12V adapter could be used without the battery, so that may mean that it does not go through the battery to the ballast. You should probably be able to replace the battery. However, It doesn't really make sense that you got 2 lights in a row with bad batteries, while no one else here has had issues. Are you sure it is not another problem? Perhaps you just have very bad luck...