This trope may have been maintained in live acting for many years due to the fact that previous entertainment genres comic strips, radio, and movies relied on the same type of humor year after year, in which the children (if any) never aged. Early television writers failed to realize the need to adapt to physically maturing characters; even in radio, a person could do the same voice, or a new performer could be inserted with little problem.
In most cases, this was relatively benign the lifespan of the programs and the aging of their younger stars rarely impacted each other.
However, in the infamous case of Family Affair (CBS, 1966 to 1971), the two intersected destructively for young actress Anissa Jones, who played 8-year-old "Buffy" on the show (not to be confused with a certain other Buffy). The program survived long enough for her to enter puberty, but the producers and writers insisted that her character and her public image had to remain a pre-pubescent child. Despite the fact that she was almost in high school, Anissa was forced to bind her breasts and play with dolls, not only on set but at press conferences and promotional appearances. The psychological damage thus inflicted is believed by many to have contributed to her death by drug overdose in 1976, a mere five years after the series ended.note
Her sad story no doubt helped to quickly discredit this trope in live-action television; most shows since the early seventies have allowed their child characters to mature naturally. The silver lining of that is at least it provides new story material for the characters as they grow into teenagers.
Sometimes this causes some absurd paradoxes to arise, particularly on long-running cartoons like The Simpsons, in which the birthdate of the kids keep changing and they have grown up in The '80s, The '90s, and the new century. In one Flash Forward, Lisa was shown as a young woman attending university in 2010, at which point, according to season 22, she was 7 years old, and by season 30, she wouldn't have even been born until after 2010. In this way, animated series can be said to harken back to the old, pre-television genres that required greater Suspension of Disbelief.