This article studies the consumption‐investment‐insurance problem of a family. The wage earner faces the risk of a health shock. The family can buy long‐term life insurance that can only be revised at significant costs. A revision is only possible as long as the insured person is healthy. The combination of unspanned labor income and the stickiness of insurance decisions reduces the long‐term insurance demand significantly. Since such a reduction is costly and families anticipate these potential costs, they buy less protection at all ages. In particular, young families stay away from long‐term life insurance markets altogether.