You've got gyroscopic stability and dynamic stability, which are two different things. You need to specify which type of stability to get a proper answer to your question.
Gyroscopic stability (Sg) is affected by bullet length, barrel twist rate, and velocity. Once the bullet exits the bore, Sg actually
increases as it travels downrange because the bullet's linear velocity decreases much more quickly than its rotational velocity. Insufficient twist rate for a bullet of given length will show up as oblong holes or keyholing at the target after very short distances (within 100 yd or less) after leaving the barrel.
Dynamic instability is a different animal and may be due to the design of the bullet itself. A prime example of this is the excessively steep boattail angle of the 168 gr SMK bullet, which can render it unstable at typical .308 Win muzzle velocities after about 700-800 yd. This effect can sometimes be overcome to a certain degree by using a faster twist rate and/or muzzle velocity, thereby increasing the distance before dynamic instability becomes a major factor.
Because dynamic instability can show up at much longer distances than that at you will typically start to see problems on the target with gyroscopic instability, the answer to your question is that it really depends on what's causing the instability as to how far downrange you might expect it to show up. For example, a 168 SMK fired at typical .308 Win velocity out of a 12-twist barrel might fly just fine out to 700 or 800 yd because the gyroscopic stability from a 12-twist barrel is more than sufficient. However, that same load/bullet may well be going sideways through the target at 900 or 1000 yd due to dynamic stability. If you fired the same load/bullet out of a 17-twist barrel, it would probably go through the target sideways at 100 yd.
If you know the velocity, bullet dimensions, and barrel twist rate, Berger's calculator will give you a pretty good idea of where you stand with respect to gyroscopic stability:
http://www.bergerbullets.com/twist-rate-calculator/