I like both of Steven's suggestions, but I also have a couple more.
%remember axis limits and rest them
my_axis=axis;
delete(LINE);
axis(my_axis);
%cheat, by setting line color to white (setting the visible property to off doesn't work)
set(LINE,'color','w')
%remember axis limits and rest them
my_axis=axis;
delete(LINE);
axis(my_axis);
%cheat, by setting line color to white (setting the visible property to off doesn't work)
set(LINE,'color','w')