All you need to do is add a forever loop around the code in player sprite that broadcasts game over. what its doing is when the flag is clicked is it checking if the game is playing one time so all you need is a forever loop and that Should fix it.

when green flag clicked
forever
if <(Game Playing) = [True]> then
repeat until <(Game Playing) = [Flase]>
if <<[(Lives)] < [0]> or <[(Lives)] = [0]>> then
broadcast [GAME OVER v]
hide variable [Lives v]
set [Game Playing v] to [False]
end
end
end
end

That should be the code