It’s possible for your access token to become invalid for a variety of reasons (expiry time passed, user changed password, user deauthorized your app, user logged out of Facebook, etc.). You should always design to account for this scenario.
If your users are active, it’s easy to get a new access token from the OAuth endpoint without them having to do/see anything. If not, you should make a plan (such as emailing them) for how you will get them to return so you can get a new access token. The scenario you’re describing is not necessarily unusual. You can find some code samples here for help on how to handle expired access tokens.