I am going to bust in on this thread as I have a similar issue.
I have a 4.3.1 site that is also not showing any updates available. I am part of the GoDaddy Managed WordPress hosting, and last night I received an email from GoDaddy saying that they had migrated my site and there was nothing else for me to do. Unfortunately, my entire site broke. After calling tech support at GoDaddy, I restored to a version before last nights update. I am working fine, but I was told by tech support that my site, since I am Managed WP, would be updated every night to 4.4.
I totally understand that this needs to occur, but I don’t know how to control this myself to see what is breaking in 4.4 or how I can upgrade to 4.4 myself.
Here is my dashboard
https://www.awesomescreenshot.com/showImage?img_id=830145
