I had a few problems with the Messaging app, so I would try switching to Hangouts for SMS just to see if that works better. Settings / More... (Under Wireless & networks) / Default SMS app. Try switching to Hangouts, start the app, and do whatever set up you need to to use the app for SMS (I can't recall what that is at the moment, but I think it asks you to confirm that you want to use the app for SMS - something like that.) All of your stored message conversations will be there.
See if that helps; let us know if it does.
