[Hide]I thought I remember someone else mentioning this, but if you open the email app, press the menu button, go to "Settings", "Account settings", and select the account you would like the notifications for, make sure the box next to "Email notifications" is checked. This will add the badge to the notification bar.
On the off-chance that it's already checked, then we'll have to hope someone more knowledgeable chimes in.
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EDIT: never mind... just re-read the first post...
Hmm.....a strange problem indeed.
EDIT2: (Sorry for the scatter-brained responses...I've been preoccupied for most of the day)
The email type shouldn't make a difference on the notification being received, but as someone else alluded to, it could affect
when it's received. Who is the email account through that you're using the email app for (Hotmail, Yahoo, etc.)?