In general, if they leave the muzzle properly stabilized, bullets become more stable as they go down range. This is because forward velocity is slowed by drag on the nose pushing into the air, while rotation is slowed by drag from fluid friction with air due to its surface speed of rotation. That surface speed is much slower than forward speed.
In feet per second, the surface speed of rotation is equal to muzzle velocity times the fraction you get dividing the bullet circumference by the rifling pitch where both are in the same units of length (usually inches). So, if you have a .308 diameter bullet going 1000 fps from a 20-inch twist. The fraction is:
pi × .308 in / 20 in = 0.048
So the surface speed of rotation is 0.048 fps for every fps of muzzle velocity in that example, and that's the speed with which surface friction with air will be working to slow rotation. In other words, the surface speed of spin is about 21 times slower than muzzle velocity in that example.
When you see a bullet keyholing, but not immediately, it is usually because the bullet is gradually describing larger circles with its nose with each turn caused by precession until that circle becomes wide enough for the sides behind the nose to catch enough air to initiate tumbling. The only exception I have experienced is with the 168-grain Sierra MatchKing which will maintain match accuracy from a 10" twist barrel until it has passed 600 yards. Then, somewhere out around 700 yards it becomes unstable. Bryan Litz says this is a dynamic instability. In effect, even though the bullet is spinning much faster than it needs to for normal stability, when it starts to drop into the transonic range, where drag bumps up, it overcorrects for air disturbances, causing it to oscillate into instability. This is why the problem shows up in a crosswind, but may not in still air. The same bullet fired from a 13" twist barrel at the same velocity can make it to 1000 yards, even in a light crosswind, so this is a weird case of overstabilization for a particular bullet shape. Other bullets, like the 175 grain Sierra MatchKing, don't do it. The thinking is that it is due to the 13° boattail angle on the 168 vs the 9° boattail angle on the 175. There are a few other shapes that may behave this way out there, but it is unusual.
What is the length of your bullet? What velocity are you actually getting? Be aware that with H110/296 that when the loading density gets below about 88%, there is danger of the loads squibbing out and leaving a bullet stuck in the barrel, which can cause disastrous gun failure if you fire the next round into that obstruction. Hodgdon used to have the warning up on the web site front page, but I don't see it now. If you want to get reduced loads with a magnum-suitable powder, Alliant 2400 is probably the best choice as loading it down simply results in not very complete combustion of a number of grains, but the bullet generally still exits.
