The English adjectives live, living, alive all have the same basic meaning – having life, not being dead (and by extension, in context of TV and radio broadcast – happening at the moment, broadcast without delay).
The typical English usage is that when directly attributing a noun, live or living is used: a living person, live TV, etc.
When used predicatively, alive is rather used: the person is alive.
So we are alive sounds much more natural than we are live (although, I guess that could be used in the meaning we are broadcasting live) – hence the translation we are alive rather than live here.
I wouldn’t deem we are live wrong (especially in the broadcasting sense) – but I’m not surprised this version was not anticipated by the contributors – you might try to report it as ‘My translation should be accepted’ next time when this exercise comes up, maybe they will accept it.