This app was mentioned in 3 comments, with an average of 1.33 upvotes
Back in the day (February-ish?) I had the same issues with MM (as did a lot of people, actually). Something rogue was using the SMS permission and preventing access to the SMS DB. On reboot (before whatever rogue app could start up), I would get a flood of incoming MMS / group messages and all the ones that wouldn't send suddenly would. After a minute or two, nothing.
Going on the assumption that this is the same / related, you can use aSpotCat to see what has permissions to SMS and deny those permissions app-by-app until you find the rogue one. You'll have to reboot after each permission denial and test. This is aggravating, I think I had like 19 that did before I found the magic one, but it's the only way I know to review it.
If you use an Android phone, you can use the App aSpotCat to list all Apps which have a specific permission.
That should help narrow down suspicious Apps quickly.