Have you checked your settings? If your server address is wrong (typo?) or ports wrong you will not be able to send/receive Email. Check with your email providers to get the correct addresses/port numbers.
Which email app are you using? Is it the stock app, gmail, etc?
Checked all the settings and ports. No apparent problems there and no typos. "Push" is set. Data sync is unrestricted. I was able to get all my emails pushed on my previous X.
Don't laugh, but I still have a couple of AOL emails, and I'm using the stock email app.
Sometimes, the emails come right through. Sometimes, they seem to disappear into cyberspace...not even a copy in the "Sent" or "Outbox". Sometimes, if I send from my GMail to both of my AOL in one email, one will come through immediately but not the other. Then, sometimes, a whole batch of email will come through at one time. Mail to my GMail account comes through immediately most times, but there have been times when they come through hours later, if at all.
I'm beginning to wonder if I have some sort of odd electromagnetic field around me that won't allow me to use the Droid X flawlessly.
That is pretty strange for there not to be a record of the emails at all. Try sending a test email and immediately check to see if it makes it to your outbox. If they aren't making it to the outbox you could have all the server settings in the world and it won't help.
Another trick I learned long ago in the cellphone programing world is to always retype the settings whenever you check them. I have had times where an unnoticed space at the beginning of settings has caused hours of headaches. Don't know if it will help you but it's worth a try.
One thing that helped me when my Email accounts messed up and that is to delete them and re-install them. That helped me. You might want to try that. Someone posted a chart listing all the POP3/SMTP settings. You might want to find it and check it out. It's a chart that they should put right in front since it has helped me and several other out tremendously.
http://community.vzw.com/t5/DROID-X-by-Motorola/I-cannot-get-my-personal-email-to-work-the-server-can-t-respond/m-p/312478#M13190
This is the site that lists all the Email info you will need. Like I said, they should glue this one right on top.