This is where having access to their written claims makes such a difference. You can see how their explanation changes, to keep the expectation fresh by implying that time has almost run out. Prior to the 1950s, the explanation was that people who were alive and could comprehend the day's events were the generation, meaning that by the 50s and 60s they would be entering their 70s and 80s. Then they explained that children as young as ten could fit that description. Then it was infants. Then it was anyone born by 1914.
Finally it was anyone who knew anyone who was born by 1914, which is where I think it went off the rails. They should have stuck with their 1995 decision to change the wording and emphasize it less, but without the sense of urgency they have a difficult time recruiting. 'Come join the religion that is awaiting the end... AGAIN' just doesn't have the same draw.