Probably, more or less, I think. (enough qualifiers for you?) Let's take Jupiter. I can think of three things that could cause it to change. First, some giant star or black hole could come by and tear Jupiter up or swallow it whole. read more
In addition, as it cools the interior will tend to condense, and that will also liberate heat. But given forever, eventually all that heat will be radiated, and the gases will freeze out. No longer a gas giant, more like a giant ice cube made of hydrogen, helium, and traces of other elements. Hope this helps. read more