Sounds like a cache problem with the messaging app. So, assuming your text message app is called "Messages", we're going to take a small journey.
Push your menu button > Settings > Applications > Manage Applications. Now you'll see 3 or 4 tabs at the top, tap "All". Scroll down to "Messages", tap it. Then tap "Clear data". Then hit home and load up your Messages app. Does it still do it?
Alternatively, you can try another text messaging app. Handcent and GO SMS are two very popular ones. Just disable message notifications in Messages app to make sure you don't get two notifications for the same text.