Something weird is happening with my Curve recently.
I hear the chime for a text or email, I go to messages (which I use to view pretty much all email/sms/etc) and I don't see anything new. New mail icon indicator no longer shows that something's not unread... but the LED indicator keeps flashing red pretty much saying I have something waiting.
Fast forward 5 - 10 minutes, I look and I have two text messages which I guess were supposedly for that chime 5-10 minutes ago. It never did this until recently.
Your device has low memory. Check to see how much free memory you have: Options > Status
Pulling the battery with the device on will be a temporary fix, but you need to read and do this: