Occasionally you will get a bullet that begins to tumble. It usually happens around the 250-300 yeard range. If it were me and I'm using factory ammo, I'd walk the target out at 25 yard increments. 225, 250, 275.
If a bullet is stabilized out to 200 yards, it will still be stable at 300.
There's only a few things that will make a bullet "tumble." (Tumble isn't even the correct word. The bullet's (in)stability is what causes the type of inaccuracy you're referring to.)
The first is if the twist rate is not fast enough to stabilize the bullet. A factory .308 with factory 150gr loads is NEVER going to encounter this problem.
The second is if the velocity is too low to get the bullet to stabilize. I've run into this when practicing with reduced loads, usually loaded with Trail Boss powder. But it shows up at 100 or even 50 yards. It never makes a first appearance at 300 or 400.
Odds are the problem the OP is seeing is either caused by shooter error (as others have said, little problems at 100 show up big time at longer distances), parallax (probably unlikely), or factory loads with a huge velocity spread (if vertical stringing is present).