Solution:
Sounds like you need to update your server’s cainfo bundle. It’s a file that contains a bundle of CA root certificates that curl uses to verify a host SSL certificate. The WooCommerce Subscriptions plugin uses curl to send a request to PayPal which it would try to verify.
First download the latest cacert.pem file. Get it from http://curl.haxx.se/docs/caextract.html. Place it in your php directory.
Then add this line to your php.ini file curl.cainfo=c:\php\cacert.pem. Obviously change the path to match your actual directory.
If you can’t get access to this stuff it’s time to talk to your server tech support.
Credit to http://snippets.webaware.com.au/howto/stop-turning-off-curlopt_ssl_verifypeer-and-fix-your-php-config/ for reminding me the procedure to deal with this problem
EDIT: WordPress 4.4 update came with updated ca-bundle.crt. You may want to try simply updating if your WordPress is not up to date.