If God exists and if God is a loving God then the most obvious, and only acceptable, answer to the question "Why does God allow suffering?" is that God cannot stop it.
But this just places the problem one step back. We would still have to answer the question, "Why did a loving God create a situation in which there would, inevitably, be suffering?" I suggest that the most obvious, and only acceptable, answer to this second question is that God didn't.
Perhaps we need to ditch or, at least, distance ourselves from, the concept of God as the original creator of matter and energy and concentrate instead upon that other ancient understanding of God where God is the bringer of order out of chaos. This would allow God to be interventionist and caring, a true redeemer. This would tie in very well with the story of Christ and our understanding of it. For such a God the greatest achievement, when faced with the suffering in the universe, would be the bringing in of a "Kingdom" where such suffering does not exist and the resurrection of all that has suffered into that Kingdom.