MCTB 2, Chapter 26, Fourth Jhana: 
"The issue of mindfulness in the fourth jhana is an interesting one, and the old texts (The Saccavibhanga Sutta: The Analysis of the Truths (MN 141), for example) say that mindfulness is considered present, but may not predominate in the way it did in previous jhanas. Just as when watching an engrossing movie there is a natural attention to the movie but we might be so lost in the story that to call ourselves mindful might be somehow inaccurate, the same applies to mindfulness in the fourth jhana."

I don't understand how the analogy of being "lost in the story" applies to the prior descriptions for the Fourth Jhana. 

I think I've accessed the Fourth Jhana as described by Ingram, and to me it was the antithesis of being lost in the/a story. 

Can someone help explain? 

I could be wrong but the way I understand this is more like mindfulness is effortless at this point. It's like mindfulness as an ACTIVITY decreases tremendously. There's a diminished conscious effort at activating mindfulness toward objects. One just sits IN mindfulness, instead of consciously bringing up mindfulness. One is so ''lost'' in mindfulness that it's like there is no conscious notion of ''I'm mindfull''.

Another way to look at it is, due to the depth and all pervasiveness of non-grasping/equanimity/dispassion, even mindfullness is seen as a stressful activity, so it takes a back seat, so to speak, even while it performs its function. Mindfulness is not searching for specific objects anymore. It's just there resting yet performing its function. It's like a neon light that's illuminates a whole room. We may not be consciously focused on the fact that the neon light performs this function. But in earlier stages it's more like we are consciously using a flashlight to illuminate things, so there is more self-consciousness and an active involvement with the light. 

In the fourth, the quality of awareness is very clear and immeditate. But just like a very clear and immediate movie on the movie screen, we can either see it as a movie on a screen... or we can get sucked into the storyline and the characters and the plot and completely forget _it_is_a_movie_.

So the important thing is to continue investigation of the moment. It seems clear and immediate -- but "who" experiences clarity and immediateness? It seems clear and immediate -- but "where" does this experience occur, is it out there or in the mind? The mind itself seems clear and immediate -- but what is the mind? Is the mind the same or different from experience itself? Is the mind inside your head or is it the same as the world that you see? How do you know? Does it make a difference if your eyes are opened or closed? Is knowing a quality of the self or the mind or the experience? Is it inside or outside? Where does this knowing occur?

It is very tempting to say in the fourth jhana "this moment is clear and obvious, there is nothing more to do except just experience it" but this is like getting sucked into the movie of the fourth jhana. For sure it's important to enjoy and soak in the fourth jhana, but for awakening, all the jhana not only need to be experienced but also investigated. Ultimately, the fourth jhana/equanimity is just another STATE that is experienced. A state has distinct qualities which allow us to say "oh, I recognize this, it is like this". But a state is more like a mental mood or a fixation, even a stagnation, rather than the actual display of reality. If we think a state is reality, we're sucked into the movie of the state and not seeing _as_a_state_.

​​​​​​​So investigating the state-like nature of the fourth jhana can be the next step for someone who regularly accessess it, including the apparent duality of the apparent meditator/self "over here" that is experiencing the fourth jhana "over there". (And of course investigate the very sneaky sense of "I am" that likes to escape investigation, including when "I am in the fourth jhana". What is in the fourth jhana? What is the "I am"?)

Hope this helps.

You are mindful, you are aware of what you are doing/experiencing as it happens, your mind is not wandering on the past or future or solving problems, it is present, but "I am mindful / this is mindfulness" is not foremost in your mind the way it used to be, so "to call ourselves mindful might be somehow inaccurate".

Another way to look at it is if you are not aware "I am mindful / this is mindfulness" then you can get "lost" in the present moment just the way you can get lost in the past, furture, or problem solving, or in a movie. 

Thanks all. I think this makes sense. 

I often recall that the stages of insight are pertinently called *-ñana for a reason. "Sanknharupekkha-ñana" is not just being equanimous, it is being equanimous + ñana: knowing about it, investigating it.

Well said Eudoxos!

Another way to think of it is that as we get deeper into the jhanas and become more absorbed or "lost" in them, our mindfulness of the greater overall situation (external environment, etc) declines somewhat.  We become so hyper focused on the object / jhana state that we lose some of the greater overall awareness that is normally present.  It's a natural consequence and tradeoff of awareness becoming highly one-pointed (vs the more panoramic view cultivated in vipassana).

Edit: that said, I reviewed the Saccavibhunga Sutta, which gives a nice overview of the qualities of the first four jhanas, and I don't see that it says anything about mindfulness decreasing in the 4th jhana, it simply notes that there is a purity of mindfulness and equanimity, the difference from the 3rd jhana being a "decline in pleasure".

https://www.accesstoinsight.org/tipitaka/mn/mn.141.than.html

Mindfulness and jhana are the same thing.
Experiencing N-th jhana doesn't lead to rapid development of mindfulness to the point you can finish your meditation and remain in N-th jhana because you are not really mindfull when meditating so you won't be mindful when you end meditation either. This doesn't only apply to 4th jhana but to all jhanas.

Best way to approach to formal meditation practice is to from time to time realign your activity which doing caused jhanic experiences to be more mindful doing this activity - read do it entirely using jhanic qualities without using your normal mind.

Practical note: if your mind does nothing when you try to use only jhanic mind then just refuse do anything and wait until you can do it using jhanic mind. It is literally impossible to change iron to gold but golden mind can replace iron mind if you give it room to breathe.