I've been trying to track down the cause of this error and I've figured out what's been causing it in my instance - I have a staging server that's protected by an HTTP authentication username / password prompt which is set in the htaccess file. As soon as I removed that password request the post schedules started working perfectly.
I didn't see this mentioned anywhere else, so thought I'd post it here for others with the same issue, even if it sounds like there are a number of different causes.