In Sierra Bullets' tests, they've learned that virtually all rifle bullets have spin stabilized by 100 yards.
If one stops and thinks about simple exterior ballistics, they'll easily learn why a 1/2 MOA system won't be a 1/2 MOA system at 1000 yards. Two main ballistic reasons.....
One's muzzle velocity spread. .308 Winchesters with a 50 fps muzzle velocity spread will have about 1/10th inch vertical shot stringing at 100 yards. Check this with any online ballistics software. Then go back to the 1000 yard line and you'll see that vertical shot stringing is about 20 inches.
The other's ballistic coefficient; it ain't the same for all bullets of a given make, model and caliber. As they ain't all perfectly balanced, they wobble a bit in flight; the more wobble the more drag they have. Sierra Bullets sees about a 1 to 2 percent spread across a batch of match bullets due to bullet imbalance. Use ballistic software to see what that spread in BC will cause in bullet drop for a given bullet at a given muzzle veloctiy.
And one environmental reason.... possibly two.....
The air on this planet's not perfectly still. Subtle wind movements exist even when flags show no movement whatsoever. These stubtle winds cause horizontal shot stringing. The longer a bullet's in the air, the more those subtle cross winds will move it. To say nothing of the slight differences in air density bullets go through enroute to the target; they ain't all the same, either.
I've done some checking on test groups fired at short and long ranges and came up with the following. Groups at 100 yards typcally get about 15% larger for each 100 yards further down range. .5 moa at 100, .575 moa at 200, .661 at 300, .760 at 400, .875 moa at 500 and so on.
One exception's when a barreled action has a lot of whip such that bullets leaving slower do so at a greater muzzle axis angle than the faster ones leaving at lower angles. The Brit's SMLE .303's are famous for this and with arsenal ammo with big muzzle velocity spreads, they shot very accurate from 700 yards and beyond. At the shorter ranges, they didn't do as well as Mauser 98 action rifles do. No wonder their SMLE's won so many long range matches.
'Tis another myth that groups keep their same angular dispersion from close at hand to all the way to some distant point. After all, don't all bullets shoot 0 moa at the muzzle?