Scheduled posts don't get any love because
save_post action isn't fired by
Switching to the
transition_post_status action instead of
save_post should fix this problem. Since that action provides the old and new statuses, it also eliminates the need for
get_post_status() and lets you move the status check logic to the start of the function. Autosave doesn't trigger either, so that check can be eliminated.
Changes made against the Git repo. Pull request awaits: https://github.com/norcross/yourls-link-creator/pull/1.