There isn't really a continue, you have to restart the job. You could create an auto-start sql-agent job that looks at recent job statuses and restarts all backup jobs that appear cancelled within like 10 minutes.
However, you might be putting more into this than is warranted. The idea is that this should happen hardly ever and if it does occur due to a scheduled outage that you should schedule it when jobs aren't running..
If your server is failing over regularly failed backups is NOT your largest problem..