How do I keep a user logged into a firebase app after refresh?

The code you now have handles the case where the user logs on. To handle cases where the user has already logged, you use theonAuthStateChanged method:

firebase.auth().onAuthStateChanged(function(user) {
  if (user) {
    // User is signed in.
  } else {
    // User is not signed in.
  }
});

Typically you only want to show the log on button in the else of this function.

Documentation: firebase.auth.Auth

---

Old answer (deprecated/archived):

The code you now have handles the case where the user logs on. To handle cases where the user has already logged, you monitor auth state. From the Firebase documentation on monitoring auth state:

// Create a callback which logs the current auth state
var ref = new Firebase("https://<YOUR-FIREBASE-APP>.firebaseio.com");
ref.onAuth(function(authData) {
  if (authData) {
    console.log("User " + authData.uid + " is logged in with " + authData.provider);
  } else {
    console.log("User is logged out");
  }
});

Typically you only want to show the log on button in the else of this function.

As mentioned in a comment, the accepted answer no longer works. The current way of checking if a user is logged in is

firebase.auth().onAuthStateChanged(function(user) {
  if (user) {
    // User is signed in.
  }
});

(from https://firebase.google.com/docs/reference/js/firebase.auth.Auth#onAuthStateChanged)