I suspect the better question is: Is it working? And it sounds like it isn't. Maybe it is the Course grade condition (which sometimes prevents completion for no reason I can figure out). Maybe it is the Manual completion and maybe it is something else. I never use any...I always use all and specify what I must have complete.
Since you have it set any, perhaps the teacher can try to check completion (I've never had success with this, but I haven't put much time it in, honestly).
First, I'd follow Mary's instructions and make sure the sync is set up properly. When the sync's not happy, no one is.
Second, wait for it to actually sync (or manually run one--I can't reliably give instructions on that; I think it is yoursitename/admin/cron.php but it does require admin permissions).
Third, if the sync hasn't resolved the problem, remove one condition at a time to see if it helps...so remove the grade condition and save, see if it syncs properly. If not, then turn the grade condition back on and remove the Manual Completion option, see if that works. I wouldn't turn off the activity (resource) completion, because that is the whole point.