https://news.yahoo.co.jp/articles/d9369f4a45806d591205c7905f7525d3ab1a9a14
image caption: "子どもは溺れる時、騒ぐわけではありません"
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borrowing the "sink below surface" from GG5 based on this.

"he's drowning!" doesn't refer to an inescapable death the same way "he's dying" doesn't - continuous tense indicates an 
ongoing/incomplete process.

I think "to (nearly) drown" works better than having "to nearly drown" and "to drown" separately because that way, we don't on the one 
hand rule out that it could mean "dying" (per the dictionaries), but it also clarifies that in general, it refers to something that can 
end either way, and normally it will be specified if it really refers to death. (e.g. as in 溺れて亡くなる). I feel that with "to drown" 
tacked on without qualifications, even at the end of the entry, learners might assume we've just formatted the entry poorly and then walk 
away with "OK, it means to drown, got it"

Really the most accurate gloss is probably "to come into a state of drowning".

@@ -16,2 +16,2 @@
-<gloss>to nearly drown</gloss>
-<gloss>to drown</gloss>
+<gloss>to sink below the surface and become unable to breathe</gloss>
+<gloss>to (nearly) drown</gloss>

OK with me.

meikyo:
泳げなくて水の中でもがき苦しむ。また、死んでしまう。

shinmeikai
泳げずに死ぬ（死にそうになる）。

gg5
 1 〔水中で〕 (死にそうになる) nearly drown; sink below the surface (of water); (死ぬ) die by drowning; drown.

"to drown" seems fine to me.

"he is drowning" does not imply an inescapable death, and "he is nearly drowning" just sounds weird; whereas, "he drowned" definitely suggests that he died (though he might have been revived), whereas "he nearly drowned" suggests that he didn't

so to me: in present, 溺れる-->"to drown" seems more sensible; whereas in past, it could go either way, but generally 溺れる-->"to nearly drown" seems to be what is meant more often?

@@ -15 +14,0 @@
-<gloss>to be drowning</gloss>
@@ -16,0 +16,2 @@
+<gloss>to nearly drown</gloss>
+<gloss>to drown</gloss>

But it doesn't mean "to be drowning" - 
that's 溺れている. I think "to (nearly) 
drown" is better.

I've just gone through about 50 examples of the drowning sense of 溺れる, and none have it meaning ending in death. In the cases where it ended in death, 溺れ死ぬ was used. If I had to summarize the meaning from them, it would be "to be downing/to be in the process of drowning." Nowhere did it seem to mean "almost".
So it seems that really those JEs and even Daijirin with its "また、死ぬ" are wrong or at best misleading.
I've suggested some slightly changed glosses, but I think basically we're on the same page.

@@ -15,2 +15,2 @@
-<gloss>to (nearly) drown</gloss>
-<gloss>to struggle underwater</gloss>
+<gloss>to be drowning</gloss>
+<gloss>to struggle in the water</gloss>
@@ -22,0 +23 @@
+<gloss>to be addicted</gloss>

My informer disagreed it actually means 
dying even when I read that bit to her, so 
I don't want to give that "また..." too 
much weight. I feel they're maybe 
referring to it when it appears in "溺れて
死ぬ" anyway.

Daijr: 泳げないために、水中で死にそうになる。また、死ぬ。
GG5: 〔水中で〕 (死にそうになる) nearly drown; sink below the surface (of water); (死ぬ) die by drowning; drown.
ルミナス: 3人の男が川で*おぼれた Three men (were) drowned in the river.

Looks like it means both nearly die and actually die. Two senses?

oboreru (辞書形) means "to be (in the process of) drowning" though

daijs, native informer

"to drown" means to "die", 溺れる doesn't.
but in 溺れて死ぬ it doesn't mean "to 
nearly drown and die". so I think "to 
(nearly) drown" is a good conpromise

@@ -15,3 +15,2 @@
-<gloss>to drown</gloss>
-<gloss>to nearly drown</gloss>
-<gloss>to sink below the surface (of water)</gloss>
+<gloss>to (nearly) drown</gloss>
+<gloss>to struggle underwater</gloss>

G n-grams:
 溺れる  	188998
 おぼれる	 36024
 溺れる者	  8322
 おぼれる者	  1641

not even close

@@ -15 +14,0 @@
-<misc>&uk;</misc>

putting like glosses together

@@ -16,0 +16,1 @@
+<gloss>to drown</gloss>
@@ -17,1 +18,0 @@
-<gloss>to drown</gloss>

GG5, 大辞林, 広辞苑

Add sense “actually drown”, alt gloss of “wallow in”

@@ -17,0 +17,1 @@
+<gloss>to drown</gloss>
@@ -24,0 +25,1 @@
+<gloss>to wallow in</gloss>