External Apple USB keyboard, Shift+Tab and Command+Shift+Tab doesn't work
Sounds like a hardware problem based on the comments. Until you can try a new one, you could get the same action by using use Cmd+Tab (holding down Cmd but just tapping Tab) to bring up the switcher, and then use the arrow keys to go back and forward.

Or possibly the Karabiner keyboard customizing app will let you remap the left shift to something else.