Frame now says that he never claimed that God's existence is logically necessary but only that God is a necessarily existing being. According to Frame, a necessarily existing being exists in all logically possible worlds. However, in possible world semantics if a proposition is true in every possible world, it is logically necessary. So if God exists in every logically possible world, then the proposition that God exists is true in every logically possible world and thus the proposition that God exists is logically necessary. Apparently, I did not misinterpret Frame after all.
Frame gives no reason except to say that the Bible says that it is.
However, few Christians have accepted this interpretation of the Bible. If Christians accepted this interpretation, they would believe they could refute atheists easily. However, most Christians have realized that refuting atheism is not so easy. Indeed, the only Christians I know who maintain that atheists contradict themselves are those few who uphold the Ontological Argument, an argument with deep flaws. This analysis does not entail that God exists in all possible worlds but it does capture one sense of a necessarily existing being.