Most asteroid deflection strategies
Most asteroid deflection strategies assume that we can intercept the object when it is at aphelion, when it is furthest from the Sun, travelling the slowest. So, the delta-vee we impart at aphelion is a larger fraction of its total velocity and therefore has a greater effect.
But imagine if aphelion is 100,000 AU from the Sun, and when we finally detect it, it's nearly at perihelion instead! How much delta-vee can we impart to an object that masses as much as Pluto and going 100,000 km/sec?