For some reason automatic background updates are not happening on my WordPress sites hosted at VPS.NET. I have several sites hosted there, and none update (sites hosted elsewhere update OK).
The latest update that didn't happen was WordPress 3.8 to 3.8.1.
I ran the Background Update Tester plug-in (V1.1) and it reported "PASS" for all the tests. There's nothing in the error_log.