3rd person shooter randomly goes invisible

Hi all,

I took the 3rd person shooter Unity demo apart and put the awesome locomation character into my own scene. Now sometimes, all works well but other times he dissapears after seemingly random movements, before reappearing. I can still see his shadow, but the actual character mesh simply vanishes, then reappears a few steps later! I thought he may have been triggering something that was making him culled or clipped, but this seems fine.. I am totally stumped as to why this is happening in my scene, but not in the generic 3rd person shooter demo..

Any help appeciated! Thanks!