Weird, I can do that no problem, and I don't actually know how! Sorry if that's not a lot of help. I actually read your post as C4 the first time, and wondered why I couldn't get it to work!

You can get something that sounds suspiciously like a very off E3 from C1 fingering too...
But then, I've never had much trouble getting (admittedly off) notes from strange fingerings on the flute, I used to play (unwittingly) with recorder fingering all the time! I can't anymore, my newer flutes mechanism isn't so forgiving.
Which brings me to another point, it could be simply that your flute mechanism doesn't like that fingering for that note, which combined perhaps with (no offence meant here at all,

) less that perfect blowing, makes that particular harmonic unusually difficult.
I dunno,