Going with the science angle, we know that the universe had a distinct beginning, so it's not "eternal" in the sense that it's always existed. The problem is in the definition of "universe". It's generally defined to mean something along the lines of "the set of all things in the universe that can, or ever have been able to, interact with one another." Anything that existed prior to the Big Bang is something that we can never know about, because it's forever separated from us by a singularity. If there was something prior to that, it would effectively be a different universe. In that sense, there may be other universes; perhaps an infinite number of other universes. But we'll never be able to interact with them.
Theologically speaking, the problem with claiming the universe will never end is that the Bible specifically claims it will. While we don't know when or how, it seems a safe bet that the Bible means to say that someday, all this will be over, and a new universe will begin that consists of paradise. It's possible, of course, that ours is not the first such universe. Perhaps God is creating universes all the time, and keeps ushering in new legions of immortal souls into his paradise. It's impossible to say, but it makes for interesting speculation.