WordPress 4.4.1 was released recently, and it fixes many things, as noted here in the official blog post. It’s a security release, so please get right on updating all of your sites (or just turn on auto-update so you won’t have to worry about it).
Of note (from the blog post linked earlier):
Some sites with older versions of OpenSSL installed were unable to communicate with other services provided through some plugins.
Think WooCommerce payment gateways, or basically any other plugin/service that communicates to outside services using SSL. If your certificate was older, it might have just stopped working.
Basically, it was unable to verify that your certificates were good, so, it just didn’t verify them correctly.
Update your sites. Always.