Everything works with 3.13.0-61 kernel, but fails with 3.13.0-63 kernel. The kernel versions 3.13.0-65 and 3.13.0-66 are also tested to fail, so there is clearly a regression between 3.13.0-61 and 3.13.0-63 builds. With 3.13.0-63 and later both SD card reader and Ethernet device are missing, both are produced by JMicron Technology Corp. so this might have to do with JMicron drivers being broken.
This kind of regressions in a stable LTS release are quite unacceptable and should be fixed. Now even installing kernel security upgrades makes me extremely worried, since the server is not in the same physical space with me and fixing kernel problems is not straightforward. The hardware used is the same as on http://us.shuttle.com/barebone/Models/XS35.html website.