Can I collect on ex-spouses term life policy?

The named beneficiaries normally collect the proceeds on a term life insurance policy. My sense is that her estate, he children or her dependent parents (or her creditors) were probably named as the beneficiaries and there may have been some provision in the separation agreement and/or divorce decree that required you to pay the premiums. That's probably why your lawyer said you must keep paying. But you should ask your lawyer that question.

If YOU were the beneficiary and she did not change the beneficiary and the separation agreement and divorce decree did not address the question, that would be an interesting legal question. In some states the divorce automatically removes you as beneficiary, in which case, without a named beneficiary the proceeds would pass to her estate, and then to her heirs under her Will (if she had one) and if not to her heirs at law. However in a few states things don't work that way. As I am not a Maine or New Hampshire lawyer I do not know what those states' laws provide.

To collect the proceeds (at least if they are substantial) the executor named in her Will would petition the probate court in her state and county of residence to accept the Will. If there is no Will, then a relative typically goes in and seeks to become her Administrator or Personal Representative. (If she had a Will before the divorce, and it named you as executor or beneficiary, in most states those provisions of the old Will would become void at the divorce. But if her new, post-divorce named you, the Court would permit you to exercise that role unless someone else strongly objected and had cause.)