Frido mentioned to me there seems to be an issue with Multisite if you use both http and https sites. The issue occurs when you do a network upgrade. The following message appears:

Upgrade Network

https://nonsecureddomain.com

Warning! Problem updating https://nonsecureddomain.com. Your server may not be able to connect to sites running on it. Error message: SSL: no alternative certificate subject name matches target host name 'nonsecureddomain.com'

This appears to be a WordPress bug, as discussed on stackexchange, and was posted as a bug:

https://core.trac.wordpress.org/ticket/31405

https://core.trac.wordpress.org/ticket/33887#comment:3