How do I make sure an enemy captain stays dead after I have defeated him?

To make sure that they stay dead, you need to behead them.

At least that's what the IGN Wiki tells me:

Death in the Nemesis System

Death is not the end in the Nemesis System: Not for Talion, and not always for the Uruks either. Whenever you kill a Captain or Warchief in Sauron's Army, there is a chance that they will survive the apparent killing blow. This can only happen if the Uruk in question was not beheaded in the finishing blow. Any Uruks that are lying down dead in the army page may come back and hunt Talion for revenge. After encountering them in the wild, they will reappear in the army page, now on their feet and sporting new scars based on their previous encounter. Some Uruks may even gain Strengths and Weaknesses depending on what happened to them.

Aside from beheading, making a Uruk captain's head explode will also make them stay dead after killing them (required skill: Wraith Finisher). With this skill, enemies that are killed by draining or Flurry Kill (on stunned enemies) will have their heads explode.

Also, you can feed a Uruk captain to a Graug (required skill to mount Graugs: Graug Hunter), which has the same effect of making an enemy stay dead.

Note that some enemy captains can't be beheaded / head-exploded by execution (e.g. those with the 'Combat Master' trait). In that case, you would have to make do with a drain head explosion (if they can be grabbed, grab them and keep on draining them until dead), Lethal Shadow Strike skill (if they aren't invulnerable to ranged attacks) or feeding them to a Graug.