@jancat: If the issue is only affecting certain contacts, then please open the Messages app > Tap the 3 dots in the top right > Settings > Block Numbers and Messages > Block numbers, and remove any relevant contact numbers from here. Tap the Back button to return to the Messages settings screen > More Settings > Text Messages, and make sure that there is a number populated in the Message Centre field > Back > Delete Old Messages On. If the messages contain pictures or emojis then try enabling Mobile Data by swiping from the top of the screen to the bottom > Mobile Data, to see if this helps.
