com.apple.WebKit.Networking continually asking to sign using "privateKey"
I had the same issue with my company SSO certificate, it's a known issue in MacOS Sierra 10.12

Temporary workaround available:

Open Keychain Access.
Select your login keychain and then the private key "YOUR ID/Company SSO Server" (Do not search for the item but find and select ... searching will not work properly to access the ACL option)


Open Keychain Access.
Select your login keychain and then the private key "" (Do not search for the item but find and select ... searching will not work properly to access the ACL option)
Double-click the key to show the key's info window select the tab "Access Control"
Click the + button at the bottom of the window and add /Applications/Safari.app
Click the + button at the bottom of the window and add /System/Library/Frameworks/WebKit.framework/Versions/A/XPCServices/com.apple.WebKit.Networking.xpc
Click Save Changes and authenticate to allow those changes
Quit Keychain Access.