That apologist is clearly trying to milk the verse for far more than he can possibly get out of it. First, the best manuscripts of Romans do not say "we have peace" but "let us have peace," making it an exhortation to have peace with God, or, more properly, to continue in the peace we were given in justification.
This leads to the second point, which is that anyone in a state of justification does have peace with God. But the fact that one has peace now doesn't mean that peace can't be broken. If one commits mortal sin, one breaks one's peace with God by turning away from him, and one loses the peace and justification one had.
Peace with God is something other than a temporary cease-fire, but that doesn't mean it can't be broken. By any standard, the United States and England have more than a cease-fire between them and currently enjoy a deep and long-lasting peace between them. Yet that doesn't mean it is impossible for them ever to go to war.
The biblical idea of peace clearly did not indicate a peace which was totally unbreakable. King David would have been shocked by the suggestion that, when God gave him peace (shalom) with his enemies, this meant they would never, ever, under any circumstances go to war with Israel again.
Thus in the divine sphere: Peace with God can be broken, but one must do something grave (something with the grave matter of mortal sin) to break one's peace with God and become his enemy. That is why mortal sins break peace with God, but venial sins don't.