Access Control settings no longer appear to save for private keys which are stored in the System keychain, so attempting to add Xcode to the whitelist there did not work for me.
In order to retain Access Control changes, I had to copy the private key + certificate to the Login keychain. This kept Xcode from bothering me when code signing archives for distribution.
Note that Xcode will halt distribution if the certificate's Trust settings are changed (e.g. Always Allow for Code Signing); you must keep these set the System Default.
I hope there is a better solution than this, because this doesn't feel right. But it works for now.