Hello and welcome to Android Central! It would help us if we knew a few things.
1. What messaging app are you using
2. What version android
3. What phone are you using?
The answer to your question could vary based on the answers to the above questions, but here's one thing to check. Go to your messaging app and hit settings. See if there is a message limit set. If so, set it to none or a higher number. Once you reach your message limit, older messages are deleted from the phone as new ones are sent and received.