Numerical solutions for the 3-body problem can be extremely sensitive to small errors. We consider how small errors in calculations can affect the lifetime of these systems. In particular, we show that numerical errors can shorten the average lifetime of a 3-body system. This is illustrated using the Sitnikov Problem as an example. To give a theoretical explanation, we construct an approximate Poincaré map for this problem and delineate the structure of the escape regions. We show that numerical errors can destroy escape regions and can cause orbits to migrate to a region in which escape is faster.