WordPress 4.3.1 site does not show link to update to 4.4

I see “GoDaddy Settings” at the top of your second screenshot. Are you part of GoDaddy Managed WordPress hosting?

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

The next time it updates and breaks, try manually resetting your plugins (no Dashboard access required). If that resolves the issue, reactivate each one individually until you find the cause.

If that does not resolve the issue, access your server via FTP or SFTP, navigate to /wp-content/themes/ and rename the directory of your currently active theme. This will force the default theme to activate and hopefully rule-out a theme-specific issue (theme functions can interfere like plugins).

Yes. I guess is it part of GoDaddy managed hosting. Mine has still not been updated to 4.4. as davidhexem from above noted that his was. I guess this is something that I need to take up with GoDaddy.

Yes, you’ll have to contact GoDaddy since it’s managed by them.