If a player dies on his/her client and there is a trigger on death with a trigger action that revives them immediatly, then all other players' clients will not activate this trigger on death (You can test this yourself by having a test message as trigger action 2). I assume this is because the instant reviving of client 1 does not not give enough time for client 2 to read client 1's death.
However, the multiplayer death/kill messages are perfectly synced up regardless of the reviving trigger action, thus I believe that with a little code rework, this bug can be easily fixed.