I'm afraid I have no news about the LinkedIn issue yet. We're still looking into it, and I'll post again here as soon as we make some progress.
I might have found what's causing your issue with Facebook though; looking at your site's source code, I see 2 sets of Open Graph Meta tags. These tags are used by Facebook to build a post preview when you share a post on FB, and FB recently started rejecting Publicized posts that included 2 sets of tags.
One of these sets of tags is added by Jetpack, and you can deactivate it by adding the following line to your theme's functions.php file:
add_filter( 'jetpack_enable_open_graph', '__return_false' );
(alternatively, you could install this small plugin if you don't want to edit your theme files.)
The other set of tags is added by another plugin or by your theme.
Could you try to deactivate one of the sets of tags, until the errors disappear in Facebook's Debugger:
https://developers.facebook.com/tools/debug/og/object?q=https%3A%2F%2Fwww.brendahash.com%2Fa-christmas-reminder%2F
http://i.wpne.ws/T2vO
Once you've done so, Publicize should start working again for Facebook.
I hope this helps.