There isn't really consensus on the matter. The government can probably compel you to stop updating the canary, but it's unclear if they can force you to publish a false update. As far as I know, it has not been tested in court.
I see. That's the compelled speech that the first amendment protects against, as outlined in the EFF FAQ [0]. Interesting.
[0] https://www.eff.org/deeplinks/2014/04/warrant-canary-faq
I couldn't stand on a street corner and swing my arm every day, and when eventually my fist collides with somebody, claim to the court "oh, I didn't assault him, I swing my fist every day in this arc and he just got in my way".
Likewise, for warrant canaries, it's unlikely that the court would consider it compelled speech when the entire premise is to use repeated speech to subvert the court's rulings.