Enable XML-RPC in WP 3.51

I upgraded three sites today from WP 3.42 to WP 3.51. Once the update was complete, I saw a message telling me that XML-RPC was disabled and that I have to go to Settings -> Writing to enable it…

…which, of course, I cannot do in WP 3.51, since this version of WP theoretically has XML-RPC turned on by default.

I tried rolling it back to 3.42 and enabling XML-RPC there. But once I update it to 3.51, I once again get the message telling me that it is off and I must turn it on in Settings -> Writing.

So, how do I turn on this service that’s turned on by default when the upgrade installation turns it off?

Any suggestions?

Charlie