My AH does this too. Has threatened several times throughout our marriage that he was going to kill himself. I started going back to a counselor last week. He said some things that helped me: For me not to be held hostage by the AH mental illness. Counselor also told me AH would more than likely be upset by certain actions I was taking to take care of myself, and therefore I should be prepared that he would threaten suicide again.
He hasn't yet. If he does, my thinking now is I'll probably tell him that is a dangerous choice he is making for himself, hang up, and call 911.