How is tonic immobility adaptive?

A gazelle goes still in a lion's mouth. Lots of prey animals do. It's called "tonic" immobility because the gazelle's muscles are tense. Why doesn't the lion kill it? The reason that the lion holds off on killing an immobile gazelle it is the reason that immobility is adaptive. Let's guess:

1. The lion is stupid. It thinks the gazelle is dead. 
2. The lion has stupid instincts. It only attacks moving prey. 
3. The lion prefers giving its family fresh (live) meat, and it bets that the gazelle won't escape.
4. Cats like playing with their food (whether for exercise, or training, or the thrill of the chase) and part of the lion wants her prey to escape so that she can capture it again. I feel like if this were the case, she'd wound the gazelle lightly to make recapture more probable. Which might happen? I don't know.
5. The lion wants cubs in the family to kill the gazelle. Does that happen? Easy mode combat simulator.
6. The lion wants to show off to other lions how healthy its gazelle was, which works better if it's alive.
7. The lion doesn't like carrying the gazelle in its mouth and hopes that the gazelle will change its mind and agree to walk voluntarily back home.
8. The lion loves carrying the live gazelle in its mouth. Happiness is a warm gazelle in the mouth. Don't knock it till you've tried it.
9. The lion is cruel and wants the gazelle to suffer in fear. Fear is the lion's bacon bits.
10. The lion is kind and wants the gazelle to have as long of a life as possible. That might not sound kind, but look at how your own society keeps suffering people alive in its beneficence.
11. Lions procrastinate just like everyone else and would rather not go through the hassle of killing the gazelle until it's absolutely necessary.
12. The lion's better nature just wants to bring the gazelle home as a friend or a pet, but somewhere down the road the lion's worse nature always rears its impulsive head.

I think #3 is the most probable ("fresh meat for the family"), but I've actually only seen #1 ("playing dead") and #2 ("attack in predators is triggered by the perception of movement") in the literature.

Immobility is adaptive in other contexts to avoid detection, of course, and you could argue that the same immobility is manifesting maladaptively when the gazelle has been captured. I think that's wrong. I think it's adaptive in gazelles at the time of capture, because it makes later escape more probable, because it keeps the lion from attacking. But why? It deserves a thorough analysis.

I'll keep adding guesses throughout the day if I think of more. Or if I read something cool. Or if I see another route by which immobility is adaptive besides avoiding detection and delaying attacks when you're in the lion's mouth. 

I guess there's the old situation of immobility being adaptive when action is being directly punished, like when arthritis causes joint pain or when people look for an excuse to slap down people they don't like, or when you've got a very vocal internal critic. That's not tonic, but it's also interesting. Yep.

Edit 1: A friend brought up Pinch-Induced Behavior Inhibition, aka the Vulcan Nerve Pinch of transporting baby cats, squirrels, mice, and rats by the neck scruff. Wouldn't it be awesome if predators were exploiting an adaptation that allows mothers to carry babies?

What about animals besides cats and rodents? The internet also has photos of adult wolves, bears, and foxes carrying their babies in their mouths, but I don't know if there's associated pinch immobility. Probably Pinch Immobility is less widespread in vertebrates than Defensive Predator-Contact Immobility, and can't explain it.

Edit 2: Any explanation that relies on the particulars of lion motivations will be insufficient, because tonic immobility is adaptive for animals on different continents with different predators. American rabbits hunted by foxes display tonic immobility too. Most of the above explanations aren't specific to lions, so that's fine, but I should say it up front. Anyway, here's a new one: Maybe tonic immobility following non-lethal contact with a predator deters the predator from further attacks not because the fox is fooled into thinking the rabbit is dead, but because the fox thinks the rabbit is sick. Lethargy is one of the symptoms of the syndrome called sickness behavior, and if you're not sure if the animal in your mouth is diseased, maybe that's reason to hold off on eating it.

At this point, I think I need to just put more effort into researching the real responses of predators to tonic immobility, and maybe predator neurology also, in order to learn whether predators have a stupid brain circuit giving them a stupid instinct to only attack moving prey, even if the prey was moving a second ago and is now sitting handily in the predator's mouth. Also, I've read inconsistent reports on whether tonic immobility is accompanied by brachycardia (decreased heart rate). If it is, then that's a small point in favor of the hypothesis that tonic immobility is a condition which a predator could confuse for death. Why the predator doesn't keep eating the animal she thinks she just killed would still be a mystery, but it would be a smaller mystery at least.

And maybe the hints I've read about tonic immobility being adaptive are wrong: maybe the prey animal's brain is just shutting down maladaptively in an extreme situation, or maybe evolution just sucks and tonic immobility is even a maldaptive response to something non-extreme like how rabbits and maybe dogs can be immobilized just by putting them on their backs in the right way, or maybe predators aren't deterred at all by tonic immobility displays, or maybe other things. I need to stop coming up with explanations for what's going on before I've gotten a thorough understanding of what's going on. Get my data first, then explain it. I suppose. And once I know about rabbits and foxes, then I'll know a little more about humans. It will be one of many dozens of perspectives on executive dysfunction in this, my Year of Solving Akrasia Forever, In Theory If Not In Practice.