I'm not in the same field, but wanted to share some advice my advisor gave me when I got all rejections the first time around in case its useful for anyone. He actually advised me not to immediately reapply the next year, as he felt I needed to do something big to make it clear that I deserved to be reconsidered. That way, when they see your application again they know why they should give you another chance (even if you weren't rejected for any deficiencies in your application the first time!) I took two years to do some research in my field (I received a prestigious scholarship), and then reapplied. This time around I received a couple of really fantastic offers. I'm not saying that everyone should take a couple of years between applications like I did (I know it can be difficult to do that), but do something and stay involved in the field so that its clear that you've taken steps to improve yourself as a candidate before reapplying. Its not that there was necessarily anything really wrong my first application (from what I know), just that things are very competitive in my field.
If it matters to you, I say don't give up. Especially to people for whom this is their first round of applications. Plenty of people reapply multiple times (that's why Harvard has a "three applications in one lifetime" rule!). Good luck, I hope you get some favorable responses from schools this year!