It basically like a snowmobile clutch. As long as there aren't significant wear grooves in the pulley faces, you should be able to rebuild the wear parts.  The way the clutch works and the possible weight shape it might not appear smooth but be working fine. It'll start to close up quickly and easily then when the flyweights start to push on the rollers it'll engage slower for a bit.

On sleds, when a belt flips it wouldn't hurt to check that your motor mounts are ok. If one is broke, then it can't keep the clutches inline.