Verizon iPhone 4 - no Exchange push?
I have a Verizon iPhone 4, and while I'm not using it with an actual Exchange server, I have several Gmail and Google Apps accounts setup as Exchange accounts that push emails to me without issue.
I would try two things if I were you:

Setup a Google account on your iPhone as an Exchange account if you have't already, and see if those emails get pushed to you. If so, you can confidentially narrow the issue down to your specific Exchange server at work.
Talk to your IT department at work and see if they have any errors logged related to ActiveSync. They might be able to determine if this problem is server-wide, or specific to your account.

Based on what I've read, this could be an issue related to your Exchange 2003 server at work. This Microsoft TechNet discussion is marked &quot;solved&quot; with an answer that links to an Exchange Team blog post titled &quot;Direct Push is just a heartbeat away&quot; that provides technical details for Direct Push/ActiveSync.