I'd guess it would come down to a) at what range does the group size go above what is acceptable for the target at hand, b) at what range the impact energy goes below what you consider acceptable for the target at hand, and c) at what range you decided you are not able to reliably compensate for angle, wind, etc. enough to put the bullet where it counts, give the above.
Case in point: I have a 700VS in .308 Win. Assuming ~1000ft-lb is a rought minimum (as in, opinions vary) for deer, the .308 should be able to deliver that level of energy to somewhere beyond 600yds, possible closer to 700. The gun is theoretically accurate enough (1.25-1.5"@300yds) to be maintain an acceptable group size out to 600-700yds (6-7" ). But in the final analysis, I don't believe that *I* at this time am capable of a 600 yd shot on deer w/ a .308, from any position under any conditions. Hopefully w/ a good deal of practice, that might change.
Another thing that ties into the accuracy thing mentioned above is at what range the bullet starts to go trans-sonic. When the bullet starts to drop below the speed of sound, it meets a great deal of turbulence, and accuracy often goes to pot in a hurry. So for a strictly theoretical answer, you could just consult a ballistics chart, and see at what range a given bullet from a given load out of that '06 goes below ~1150fps (roughly speed of sound) and there you go.