Comment by LorenPechtel

The problem is that the planets aren't standing still.

You want to do an optimum burn for Earth -> Mars? Compute an ellipse such that one end touches Earth's orbit, one end touches Mars' orbit. Oops, Mars isn't going to be there, you wait. Once every 26 months you will find that half an orbit later Mars will be there, then you burn. We call this a launch window.

26 months later they will line up again, but neither Earth nor Mars are where they were before. A spacecraft in this second window will never pass anywhere near a crippled spacecraft that flew in the first window. Nor could they do anything but send a report if it did happen--if you're doing efficient burns you don't have the fuel to go to somebody's aid.