The "Missed schedule" is not related to Jetpack or WordPress, it happens when your server is not able to trigger the wp-cron process responsible for publishing the posts. You can read more about it and find a solution to this issue here:
http://wordpress.org/support/topic/scheduled-posts-still-not-working-in-282?replies=19#post-1175405
You could also try to use this plugin:
http://wordpress.org/plugins/missed-schedule/
Jetpack Publicize, however, should work whether you publish posts immediately or schedule them to be published later.
Could you post your site URL here, so I can have a closer look?
If you want it to remain private, you can also contact us via this contact form:
http://jetpack.me/contact-support/