You're the victim of a common "false belief." Rifle bullets do not become less stable at longer ranges--unless the range is so long the velocity drops to the "transonic" range, where they start traveling below the speed of sound. The ttransonic velocity varies with elevation, termperature and other factors. but is generally around 1100-1200 fps.
At retained velocities above that, bullets actually become more stable as range increases. This is because stability is due to two factors, the air flowing over the front of the bullet (which tends to destabilize the bullet) and the rotation from the rifling (which when faster tends to stabilize more).
At the lower velocities of longer ranges, the air-flow over the front of the bullet decreases considerably. Meanwhile, the rotation of the bullet due to the rifling doesn't slow down nearly as quickly. As a result of these two factors, bullets become more stable.
Many shooters, however, don't realize this, due to shooting relatively larger groups at longer ranges. However, this is not due to destabilization, but the effects of wind-drift, which increases at roughly twice the rate of range: If a bullel drifts half an inch at 100 yards in a certain wind, it will drift around two inches at 200, and eight inches at 400. But this has nothing to do with bullet stability.
