Cannot Connect to Game Center Server

When I open the Game Center application on my iPhone 6 running iOS 8.3, it prompts me to login. When I attempt to do so, it renders this dialogue box:

Could not connect to Game Center server.

In light of popular resolutions posted online, I went to Settings > Game Center and logged out. When I attempt to log back in, I receive this dialogue box:

Unable to connect to server. The operation couldn't be completed (GKErrorDomain error 3.)

I checked Apple Server status and all servers, including Game Center, should be up.

Any advice?