MBA 11" backlit keyboard no longer lighting automatically

The backlit keyboard on my MBA 11" is no longer responding to the "automatically illuminate keyboard in low light" option in System Preferences. I can control the backlights manually with F5 and F6, but they don't come on automatically in the dark (easily testing by covering the camera).

Originally, the F keys would even be completely inactive, with a line appearing across the on-screen brightness display to say the control was on automatic, but that doesn't happen any more.

I have reset the SMC, but that has changed nothing. The automatic brightness control on the display works fine.