Mars apparently revolves on an unstable axis. They say this is what will ultimately happen with Earth once the Moon drifts far enough away. The Moon helps keep our 23.5 degree tilt angle stable. And it's slowly leaving us, at the rate of about 2 inches per year.
The Moon draws rotational momentum from the Earth; if that lasts long enough, the Moon will cease to be a satellite of the Earth. If it isn't enough, the Earth and Moon will be locked in a face-to-face resonance. The loss of the Moon will not cause instability, it will if anything lead to greater stability -- after the Moon wanders away far enough to wander off. The transition will be, uh, a little rocky, and that will last a while.