Full-Service subscription expired; doesn't backup anymore

(Note: I already sent a message to support about this, but since it says only customers with valid Full-Service subscription can get help I’m not sure if I’ll get a response.)

I received an email that our support contract has expired, and that as part of that we will no longer get email notifications about the backups. That’s no big deal right now, so I haven’t renewed as of yet. The email we received says:

If you do not renew, you can still use the version you currently have, but your will stop receiving the latest SQLBackupAndFTP updates, will have no access to direct email support, no access to Web Log and will not be able to use our mail servers for backup notifications.

Our backups are now immediately failing with an error message which says:

Job execution error: Full-Service subscription has expired. You will stop receiving email notifications in 6 days. Renew the subscription to continue using the Automated email notifications for your backup jobs…

According to the email we received, we should still be able to do backups. So my question is, how do we get our backups going again?

I heard back from the support team, so posting their response in case anyone else has this problem in the future:

You are absolutely correct - your backups should continue without interruptions. However we consider a job as “Failed” if any of the steps (including sending email) has failed. To resolve it you can either upgrade or set up your own SMTP service in “Advanced email options”. To upgrade please login to your account…