We have a 6' wood privacy fence. "Some" of the posts, (that were all cemented in), have raised (popped straight up). What can cause this - and any ideas for repair?

If the hole was funnel shaped, it can do that, I like to have the bottom of the hole bigger than the top to prevent this, Some Large rocks can help hold in place if placed in hole and mixed with the concrete.

Was there frost in the ground when they started to rise?

When did you first notice that some posts were rising, what month and where do you live?

...any ideas for repair?

If holes are not deeper than the frost line for your area, you'll need to pull the posts, and redig holes deeper and larger than post. Pour a 8-12" concrete footer block in bottom of hole, plant post, and then fill remainder of hole with packed gravel.

IF concrete has stabilized, you might also cut off the posts and attempt drilling out the post portion still in the concrete, filling drilled out hole with more concrete, attaching a post anchor, and then reconnecting the posts; or something similar.

I'd go the first route if I needed a sturdy fence.

The main thing is the frost line... if you arnt below it... nothing will last very long. If want to fix it right... pull and re-set your posts.
Mike