Given Pearson correlation coefficient:
$$r = \frac{\displaystyle {}\sum_{i=1}^{n} (x_i - \overline{x})(y_i - \overline{y})} {\displaystyle \sqrt{\sum_{i=1}^{n} (x_i - \overline{x})^2(y_i - \overline{y})^2}}$$
There is probably some $n$ at which an addition of 1 case has a negligible effect on the calculated correlation, unless that case is an outlier, I suppose.
Is there a way to establish if given a group of $n$ cases and a correlation coefficient, that for some number $s$ of new cases, the new $r_{n+s}$ is let's say 98% identical? Assuming those new cases are not extreme outliers of course $(|z|>3)$ and are normally distributed.
Or would I have to compute it on a case by case basis?