Filaman,
You have stability backward, but many people do. Spinning bullets do not become less stable as they slow down.Instead they become more stable--at least at the ranges most people hunt big game.
This because there are two opposing forces on spinning bullets--the spin, which gyroscopically stabilizes the bullet, and air pressure on the front of the bullet, which destabilizes them. The rate of spin has to be sufficient to overcome the frontal air pressure (and yes, these are exactly the same forces at work on a thrown football).
The rate of spin produced by the rifling and muzzle velocity drops very slowly as the bullet passes through the air. The bullet's velocity, on the other hand, drops comparatively rapidly, which reduces the air pressure on the front of the bullet, making it more stable.
The main reason many shooters think a bullet destabilizes as it loses velocity is wind-drift--which increases about twice the rate as range. For instance, if a given bullet drifts 2 inches at 200 yards in a 5 mph wind, it will drift about 8 inches at 400 yards. This effect occurs even in very mild breezes, so mild many shooters don't even bother trying to compensate for wind-drift, instead aiming directly at the target. This results in larger groups at longer ranges, which many shooters believe are the result of bullets losing stability. But they're not.
There is an exception as bullet velocity drops below the speed of sound, about 1125 fps at lower elevations, which creates some turbulence. That's why .22 rimfire match ammo typically has a muzzle velocity slightly below 1100 fps: They leave the muzzle at less than the speed of sound, so don't drop through the "transonic zone," and long-range centerfire target shooters try to keep their bullets supersonic. But the velocity of most modern varmint and big game bullets does not drop anywhere near the speed of sound at typical hunting ranges, so become more stable during their entire flight.
