You could buy a permanent life insurance policy and never worry about the coverage expiring. But the premiums are much higher than the premiums for term insurance, and young families who start out with permanent insurance frequently buy too little coverage because that's all they can afford.
A more cost-effective way to extend the coverage is to layer policies. For example, buy a 20-year term policy for the bulk of your coverage, that allows you to get a death benefit large enough to protect your family while your kids are at home and you are making mortgage payments. Then layer it with a policy with longer term and smaller amount.
If you want some permanent coverage too, you can add a guaranteed universal life (GUL) which has much lower premium that other permanent life insurance policies but you can keep for your lifetime.