Can someone maintain life insurance on the their ex-spouse.

Life insurance depends on contract, not on marriage/divorce. As long as a spouse or former spouse is the designated benefiticary, he or she will receive the benefits in the event the insured passes away. (Note: if the estate is the beneficiary, then that would be altered by divorce, since a former spouse will not collect from the estate in the way a current spouse  will.)

However, note  that the beneficiary can be changed at will--it's just a matter of paperwork by the insured.

In order to own and pay for life insurance you must have what is known as an "insurable interest." Insurable Interest has been defined as the requisite connection between the owner/payor and the person whose life is insured.  This requirement usually demonstrates that the owner/payor will actually suffer some kind of loss if the insured dies; for example, as in the case of a financially dependent spouse or former spouse and children in the life of a former spouse.  If you receive alimony or if you are receiving child support then you have an insurable interest;  otherwise, you probably do not.  You will need to see how the final divorce decree addresses this issue. To be certain of your rights under state law, you should discuss this matter with a local attorney or at least contact the Department of Insurance.