How can suffering from natural causes be reconciled with an omnimax god? The christian god is omnipotent, omniscient and omnibenevolent according to all christian denominations I know of. These attributes seem to be contradicted by all the suffering we observe here on earth. Why does God not intervene to prevent suffering if he knows of it (omniscience), has the means to prevent it (omnipotence) and is benevolent?

The most common explanation I heard was that the free will of humans is responsible, but this questions is not about that. There is a lot of suffering caused by natural catastrophes, illnesses and so forth. I want to restrict the question to natural causes where we have no means to prevent them, such as e.g. incurable diseases.

How can one explain the presence of inevitable suffering not caused by other humans, but by natural means, if God is omnipotent, omniscient and omnibenevolent?
You're looking at the question from a mortal perspective, whereas God has an eternal perspective.  He put us here not to be here as an end unto itself, but to prepare us for what comes after this life.

In the Sermon on the Mount, we are commanded to be perfect "even as your Father in Heaven is perfect."  God is perfect because he never uses his power to do anything which would be wrong, no matter how tempting we might make it.  But we are imperfect and prone to physical and spiritual problems of every kind in this life.  In order to grow and attain a Godly level of perfection, we need practice.  We need for things to go wrong so that we can learn to deal with them correctly.  Otherwise, we can never become the kind of perfect people that the Gospel is supposed to lead us to be.