You can request a manual review by using an appeal. You get two appeals, each on a 15 day counter before you can use them again. If you are not seeing the button to appeal on your rejected contribution, then you do not have one available to use.
You are invited to post screenshots of nominations that have been rejected by the automated process if you would like our advice on whether it would be a good candidate for appeal. I know that you have been discussing one of these here: Art Unique - Rejet POI