If you registered the domain through us, yes. We renew it for another year and charge your saved card without you doing anything.
To check, open Domains and click the domain. Renews means auto-renew is on. Expires means it's off and the domain will lapse on that date. Use the Auto-renew setting on the same screen to change it.
If a domain lapses it stops working, your app is no longer reachable at that address, and after a grace period the name goes back on sale to anyone.
Renewals usually only fail when there's no saved card or it has expired. If that happens, open the domain and press Renew domain to pay for another year. You can use that button any time you want to renew early.
Domains you connected from another registrar renew wherever you bought them. We can't see their expiration date or renew them for you, so turn auto-renew on there.