Having to guess but, your Galaxy has to be set up to access your e-mail account on the internet. Can you visit your e-mail provider's website and log into your e-mail account from there ? If so you can see whether you still have the older e-mails or not. It's possible the app on your Galaxy no longer shows older e-mails; but only checking on the site will tell you if they are still there.
What e-mail account provider do you have ? Do you access the account from anywhere else, such as a desktop ?