I have exactly the same problem here: “Update Failed: Connection lost or the server is busy. Please try again later.”. After receiving this error message, I couldn’t even get back to the admin back-end site and also got “Server Connection lost” error message page on the screen. This is the localhost testing site, the path should be like: “localhost/xxxx/wp-admin” on the browser, but after the error occurred, the path became: “www.localhost.com/xxxx/wp-admin”, very weird and this never happened before but updating to the current WP version 4.7.
I have to use previous back file to restore and get back to the site again. Not every plug-ins have the same problem, but some of them. I tried several times, so now I stopped updating the “unsure” having problem ones.
I did not find any solutions or post anywhere, if I missed it or anyone have any solutions, please help!! Really appreciate it!!