One of my 560's was doing the same thing and I actually found that after I changed my wires, cap and rotor she fires right up regardless...have you checked the wires/wire ends? and also have your coil checked . Mine was found to be weak and I just replaced it last weekend which also helped with the throttle response issues I had. 322k miles and kickin' huh? MAN! I thought mine was doing good with 219k on one and just over 200k on the other. Your car gives me even more hope!
Good luck...
Alan