You can delete the entire database. It sounds like it may be corrupt.
Connect your device to you PC, launch DM, go into Backup/Restore and select advanced. On the right side you should see the device databases. Highlight SMS Messages and click the clear button. That will clear your SMS database.
After you've done that, send yourself a test SMS message and see if you can delete it.
The difference between stupidity and genius is that genius has its limits.
When you take things for granted, the things you are granted, get taken.
Even a mosquito doesn't get a pat on the back until it starts to work.
Too many people miss the silver lining because they're expecting gold.
[BES 5.0.3 / GroupWise 2012 HP2]