Hello amrubal,
Thanks for reaching out using Apple Support Communities!
We understand you're trying to view your old messages but they don't seem to be loading all the way. We can help you look into what might be causing this.
Does this happen with all threads, or only certain ones?
Do you have plenty of available iPhone storage space on your device?
Are you using iCloud to store your messages? Let's verify your settings with these steps: Use Messages in iCloud
We can also make sure your connection is working as expected and that you're using the latest iOS version: Update your iPhone, iPad, or iPod touch
Cheers!