HTC Hero :: Email Sync Problems

I'm having some issues with email syncing on my Hero. I like the HTC email app and widget, so I set up the Mail app to sync to my Gmail account via exchange (for the push functionality). Well, it does not work very well and sometimes not at all.

Here's some symptoms:
- If new emails do somehow make it to my phone, they are marked unread. I read them and they are then marked read. Then after about a minute, the phone syncs again, and they are then marked unread all over again. It's a continuous cycle until...
- The mail that does make it to my phone is sometimes randomly deleted. I verified this by logging into gmail from my computer and messages that were on my phone are now in the trash folder.
- Most mail does not even make it to my phone.

It started out working just fine for about 6 hours or so and then the problems began. I've tried deleting the account from the phone and starting fresh. It does the same thing even on a fresh account now.

I tried to just use the Gmail app since I was tired of trying to deal with it. The Gmail app does not push either. I have to manually sync it. It will never sync on its own. I have the option checked in data synchronization to sync gmail. Is there some other option I need to check to make sure that it pushes new mail?

All I want is to receive pushed email. I need the instant notification of new mail. I know that it is capable of doing this.