I think its device dependent. On my HTC One (non windows phone) in the message you could select it and secure it via passcoded sector. It moved there and then I deleted all the rest.
The protected ones stay. You can however remove them if you change your mind.
My iphones keep messages and videos forever if I activate the setting.
Device dependent is my guess.
Right now there is no setting to "lock" text messages to prevent them from being deleted.
There's a suggestion on the Windows Phone User Voice side requesting the ability you can vote for; Create a way to lock/save texts from being deleted – Feature Suggestions for Windows Phone