Be sure to check your Fetch setting (Settings>Fetch New Data). Push should be ON to receive email from Exchange automatically. You can turn Push on or off as you wish. Keeping it on uses more battery power, because the iPhone receives the email immediately. When you turn Push off, push accounts fetch the email instead, and you can set the timetable for fetching, or set fetching to manual.
You can also set Push or Fetch settings for individual accounts. Scroll the Fetch New Data screen to the bottom and touch Advanced. Each account in the list shows Push or Fetch, depending on whether the account offers push email or not. Touch the account to change its settings separately.
You can find these and other tips in my iPhone app, "Tony's Tips for iPhone Users Manual" in the App Store (search for "Tony's Tips" and it pops up).