Alternating play in life and death
A typical but unstated assumption when talking about the status of groups (alive or dead, connected or not, etc.) is that of local alternating play. It may be possible to construct contexts in which this assumption is invalid. However, given how humans used language, that this assumption is appropriate. In Combinatorial Game Theory terms, it amounts to the assumption of independence.
Kos have a way of destroying independence. For instance,
Black can capture this White group while White takes and wins a two move approach ko.
But it is fine to say that the White group is alive. It's just not unconditionally alive. ;-)
Many otherwise live formations can be killed if the attacker gets one or more extra moves as an unanswered ko threat.