Cannot export private key from System.keychain with Keychain Access or command line

I'm trying to export a private key from System.keychain in Keychain Access. I've tried running Keychain Access as a root. No matter what, I always get the following error.

When I try to export the private key via the command line I get the following.

security: SecKeychainItemExport: The contents of this item cannot be retrieved.

Most likely, your key was imported with -x option for security import:

<...>
-x      Specify that private keys are non-extractable after being imported.
<...>

When you try to export a key, Security Framework checks whether this attribute is set and refuses to export the key.

Of course, the key is still there and you might be able to find a way to extract it (see this question).