In theory, down range shot consistency (sometimes a/k/a "accuracy") is an exercise in angles. And if you extrapolate this theory, a shooter who can consistently shoot 1" groups at 100 yards (i.e., 1 MOA) should be able just as consistently to shoot 6" groups at 600 yards and 10" groups at 1,000 yards -- both of which are also 1 MOA.
Regrettably, this theory breaks down when we try to do it. Here's why. Each shot that is fired is affected in it's ultimate trajectory by a long list of factors. At short ranges, like 100 yards, shot-to-shot inconsistency is dominated by one set of factors. Most of those involve shooter technique: trigger discipline, sighting error,breath control.
Once our stalwart shooter has mastered technique, however, two things happen. One is the familiar engineering principle that as a dominant error factor becomes controlled, other factors will become dominant. The other is that as range increases, a number of factors whose contribution to short range error is in the noise now become more important because their coefficient of contribution is non-linear.
A major issue with long range shooting is wind effect. Wind effect on bullet flight is the product of vector magnitude and time of flight. We can estimate time of flight with some precision, but it is virtually impossible to measure the net effect of wind vectors over 1,000 yards. Another knotty factor is BC error. Handloading books usually give one value for BC (Sierra at least usually gives two or three)a, but actual BC varies with instantaneous bullet velocity, which is continuously changing between the muzzle and the target. So, you can chrono your load, look up the bullet maker's published BC value, and then calculate how much holdover is required to hit a 600 yard target with a 200 yard zero'd rifle. If you do this a few times you will find that it never works out. And at 600 or 1,000 yards, BC error can be a lot while it 100 yards it is probably undetectibly small.
We'll skip mercifully over a bunch of other factors, such as muzzle velocity variability caused by ammo varability, propellant temperature sensitivity, and other contributors, barrel resonance, precession, trans-sonic turbulence, and even the Coriolis Effect. Whole books have been written on the subject. Frankly, reading them is less fun than popping off a few long range shots. But, if nothing else, understand that short and long range shooting are two different animals, and adjust your expectations accordingly.