How does the son (R.L.) die?

The truth is that the most startling thing about the brother's death is the complete lack of exposition of its circumstances. Nobody follows up, asks or even hints at what might have caused it. I think this is a nice move for Malick to pull because it gives the story an almost biblical sense. As a predominantly spiritual work, dwelling on details like how exactly a person dies are simply distracting. Like the "she's my sister" trick and locusts in Days of Heaven, it's clear that Malick is taking some cues from the Old Testament here. The Old Testament almost never goes into detail about the circumstances in which a person dies, it's much more interested in the spiritual lessons surrounding the death.

The lessons of the brother's death and how the family comes to grips with it are not meant to be contingent on any particular circumstance, they are meant to be universal and timeless. People die all the time, often in ways which we find unjust. The issue to deal with isn't how they died, it's how we relate to it. And by breaking our narrative expectations and hiding the cause of death, Malick draws our attention to this point.

Which isn't to say that I'm against speculating about what might have killed him, it's just that taken in context, it's clear that the film is intentionally drawing our attention away from that question.

It makes the most sense, if one assumes suicide. That better explains why the eldest son blames the father; in other words, formative moments in the middle son's life, and a lack of affection from the father towards his sons, are suggested as being contributors to the death...

The following, lifted from thepointmag.com, is poignant and insightful:

We cannot leave alone the question of R.L.’s death, though. As a suicide, it is much more significant than random death in military combat, since it relates to the sorrow and meaninglessness of existence... I think Jack’s memory of R.L., his playmate and childhood companion, coupled with the reality of his suicide, provokes his own existential quandaries, just as Larry Malick’s suicide is a ghost haunting Malick’s thoughts on meaning in his films.

Though I have no evidence, I assumed the son died in some military-related incident because it was delivered by telegram which is a seemingly cold, sterile and impersonal fashion to deliver such news. I just assumed the implication was this was a death related to military activity.

I know that you are not supposed to interpret a director's work as their autobiography, but if you read a little about Terrence Malick I think it becomes clear that he has included many elements of his own life. His brother was a creative, sensitive guitar player who committed suicide at about 19 or 20. The movie often shows a young boy with significant burns on the side of his head, and Terrence Malick's other brother was also burned. There is also a suggestion of a noose in the beginning of the movie. Because of the evidence, I think it is reasonable to assume that R.L. committed suicide.

In the early days of the Vietnam War death notifications became so commonplace, and the military so unprepared for the great numbers of death notices that they were delivered by telegram. The practice was later changed and representatives of the deceased military service would personally deliver the death notification.

The telegram delivery is a pivotal scene because it shows how "wrong" a life is that simply focuses on nature and ignores grace. What could be worse than a strangers handing a note to a mother to read alone that her 20 year-old son was now dead.

Similarly, the grandmother stating to the grieving mother, "people die and life must go on" is so devoid of grace that we see ignoring the grace aspect of life, however inconvenient, will even override nature. This is reinforced by the dying dinosaur scene when the dinosaur leaves the injured dinosaur without killing it. Grace has its proper place in nature.

To be honest, I gained the impression from the film that R.L. jumped off that waterfall into the water.

That was just my opinion though.