In theory, you should have a declining need for life insurance as you age because fewer people remain dependent upon you for income support. Exceptions would be protecting a business entity or paying taxes on a large estate for heirs. If the purpose of buying life insurance is to pay estate taxes, then you’ll need permanent life insurance, which is in-force as long as you live and pay the premiums.
If you want more than a death benefit from your life insurance policy and like the idea of a long-term savings account (not insured by any federal agency) or investment, you might consider cash value life insurance such as whole life insurance, universal life or variable life. But be prepared to pay much higher premiums per $1,000 of coverage because you are now funding a cash value account and paying fees and expenses.
In many cash value policies, the annual premium does not increase from year to year. Universal life policies allow you to fluctuate or even skip premium payments, which in turn adjusts your death benefit amounts.