Quote From Maz1:
rewt, they are reluctant on providing feedback.
Press them. If no success, you need to try and get feedback from someone else who is an academic and preferably in the same subject area. Can you contact a former professor and ask them to review it and provide you with feedback?
Your application might be great and still get rejected but feedback will help you know whether this is the case or not. If it is then you need to keep trying but otherwise you can work on improving it.
I'm not sure about GRE (have just googled). I mean surely you know if you have a good grasp of the area you're writing about? Reading relevant and recent papers in the field and seeing how your writing and the issues you are writing about compares / fits with those might be a better indicator and way to improve.