An objective answer to the OP's question can be reached by setting up some paper plates and firing away at different ranges, positions and wind conditions. At the point where you are beginning to miss this heart/lung sized target, you have reached your max. That point is likely much closer than you think.
A subjective answer is more difficult to reach - how comfortable are you in causing a magnificent game animal to escape only to die painfully in the following hours and days? If this posibility concerns you, conduct yourself accordingly. If that does not matter to you, than fire away but understand there is a price we all pay for your actions.
