But is it not a sign of unbelief when the promises of God are not firm enough for us, without support?

It is a sign of the smallness and weakness of faith, and such is indeed the faith of the children of God, who do not, however, cease to be faithful, although their faith is still imperfect. As long as we live in this world some elements of unfaithfulness remain in our flesh, and therefore we must always advance and grow in faith.