Not changing automatic transmission oil on time won't result in immediate transmission failure, however it will greatly shorten its life. With regular fluid changes transmission could easily last lifetime of the car, however old fluid will result in a very expensive fix around 8-10 year mark. It is much cheaper to change transmission fluid and filter than having to pay for new transmission or a new car.

During 90s 'lifetime fill' transmission fluid resulted in failures, lawsuits, some recalls, and adjusted maintenance schedules. These days, no manufacturer would make such claim. Change your transmission fluid every 60K or 5 years.