This is a problem I have had since day 1 of upgrading to Windows 10 (August 2015). Cortana thinks she's my wie and totally ignores me! That's not strictly true - if I press the mike button then say "Hey Cortana" she can be quite helpful. If I DON'T press the mike key first then she is deaf to all my pleas including "Hey Cortana" and ess complimentary statements. I have always assumed this is just the stupid way things are and that everybody had to go through both steps. Brian has just informed me this is not so and directed me here to seek help.
I have checked that "Hey Cortana2 is enable