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> 生きるか死ぬかの問題だった。  
>  It was a question of life or death.  
>  飲み水が、一週間分あるかどうかだった。  
>  It was _a question of_ whether or not there was a week's worth of water.

The only way I can make sense of this structure is to assume that 飲み水 is the
subject of ある. I'm parsing it like this:

> [ _問題は_ ] [飲み水が、一週間分あるかどうか] [だった]

The comma, and the lack of the topic is making me think that 飲み水 should pair
up with だった, but I can't make a meaningful parsing if that is the case.

I know it is common to omit the topic and I also know that commas don't serve
the same grammatical purpose as they do in English. I'd just like to check
that my understanding of this sentence is correct.
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grammar parsing
Understanding ～かどうかだ
> 生{い}きるか死{し}ぬかの問題{もんだい}だった。
>
> 飲{の}み水{みず}が、一週間分{いっしゅうかんぶん}あるかどうかだった。

Overall, you have a good understanding of the passage.

The first sentence tells us right away that there was a rather serious issue
and the second explains exactly what the degree of the problem was.

The comma in the second sentence is completely optional. It is not needed as
far as grammar. IMHO, the author used the comma to make the sentence look more
dramatic by "forcing" a short pause there.

「飲み水が」 modifies 「あるかどうか」 and not 「だった」.

The omitted topic is 「問題」 here, which is already mentioned in the first
sentence.

My own TL:

> "It was a matter of life or death."
>
> "It was at the level of whether or not (our) water supply would last a
> week."
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Conclusion first, the _grammatical_ topic of the second sentence is **not**
問題(は). I know this is unusual, but in this case, adding 問題は at the beginning
of the sentence will dramatically change the meaning of the original sentence!

>   1. 飲み水が一週間分あるかどうかだった。  
>  There was at most only a week's worth of drinking water. / There was
> drinking water that might or might not last for a week. / There was some
> drinking water, but I was not sure it would last even for a week.
>   2. **問題は** 飲み水が一週間分あるかどうかだった。  
>  The problem was whether or not there was a week's worth of drinking water.
>

I think you already know how the second interpretation works. ～かどうか forms an
embedded question, "whether or not ～". I was initially unaware of this, but
the second interpretation would also be perfectly valid in a certain context.
For example, if he knows he will be rescued after a week, and if he has
everything to survive other than drinking water, then the only problem left is
whether or not there is enough water for the next seven days.

But the actual story is not like that, and that's why you asked this question,
right? :) Perhaps he had no idea when he would be rescued; he might have to
wait much longer than a week. Thus the correct interpretation is **1** , and
you must not add 問題は at the beginning for this sentence to work. You have to
be able to interpret this sentence as-is, without adding 問題は.

So, how does the first sentence work?

～かどうかだ or ～かどうかです has a usage that is a bit different from "whether or not ～".
This is a little colloquial and I don't know how to normally translate this,
but the basic idea is something like "may or may not", "fifty-fifty chance",
"not certain yet", "depends on chance", "on the borderline between success and
failure", or such.

Some examples:

>   * ここから富士山は見えるかどうかです。  
>  From here, you can see Mt. Fuji if you are lucky. / Sometimes we can barely
> see Mt. Fuji from here. / There is a chance we can see Mt. Fuji from here.
>   * 彼は合格できるかどうかです。  
>  He is on the borderline between pass and fail.
>   * 急いでいるが、間に合うかどうかだ。  
>  I'm in a hurry, but I may or may not be able to arrive on time.
>

Sorry for the loose translation, but I hope you now understand how to
interpret the original sentence without adding an imaginary topic.

Finally, if we do need to start this sentence with 問題は without largely
changing the original meaning, we can say this:

> 問題は[飲み水が一週間分あるかどうか **だということ** ]だった。  
>  The problem was the fact that I had only a week's worth of drinking water
> (at most).

I simply enclosed the "かどうか" part with a nominalizer(?) だということ.

* * *

(EDIT history: Rewrote almost everything, but my opinion is the same. I hope I
have explained this issue better now.)
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# English

> (1) 生きるか死ぬかの問題だった。  
>  _It was a question of life or death_.  
>  (2) 飲み水が、一週間[分]{ぶん}あるかどうかだった。  
>  _It was a question of whether or not there was a week's worth of water._

If OP thinks that "the only way I can make sense of this structure of (2) is
to assume that 飲み水 is the subject of ある. I'm parsing it like this: [問題は]
[飲み水が、一週間分あるかどうか] [だった] _It was a question of whether or not there was a
week's worth of water_ ", I think OP interprets (2) as
"１週間分の水があれば助かる、それより少なければ助からない _If there was a week's worth of water I would be
saved and if there was water less than that I would not be saved._ " I also
interpreted it as OP did for a moment and thought that it was correct that the
OP added "問題は" at the beginning of (2).

However I think it's impossible that such a sentence as (2) could exist
logically under actual circumstances.  
The interpretation of OP is valid only if you know that the relief team will
arrive in a week or if you can reach some place where there is sufficient
water within a week.  
Do you really measure whether the amount of water at hand is a week's worth
when you are in a situation "生きるか死ぬかの問題だった _It was a question of life or
death_ " as the sentence of (1) says?  
The meaning of "飲み水が、一週間分あるかどうかだった" is not "It was a question whether or not
there was a week's worth of drinking water" but I think "Only sure thing was
that there was at most a week's worth of drinking water at hand."

As the conclusion, the whole meaning of (1) and (2) is that "It was a question
of life or death. Only sure thing was that there was at most a week's worth of
drinking water at hand. Nothing other than that was sure." or "It was a
question that I had to live only with the amount of water worth for a week or
so at hand when I was neither sure whether a relief team would come or not nor
sure whether I could reach/found the place where there was plenty of water
before the water at hand was consumed."

# 日本語

> (1) 生きるか死ぬかの問題だった。  
>  (2) 飲み水が、一週間分あるかどうかだった。

質問者は(2)を「１週間分の水があれば助かる、それより少なければ助からない」と解釈しているように思います。  
私も、一瞬そのように思い、(2)の最初に質問者が「問題は」を補ったことは正解だと思いました。

しかし、どう考えてもそのような文は論理的に存在しないような気がします。  
水が１週間分あれば助かるとは、１週間後に救援隊が来ることが分かっている場合あるいは、１週間あれば水のあるところにたどり着ける場合の論理です。(1)の「生きるか死ぬかの問題」である時に、水が１週間分あるかどうかを計測しますか。

「一週間分あるかどうか」は、whether or notではなく、「水が **約** 一週間分ある _there is about one week's
worth of water_ 」という意味だと思います。

結論として、  
(2)を含む全体の意味は、「手許{てもと}にあるのは、水が約１週間分の分量あるという事実だけだ。これだけで果たして生き延びられるだろうか。救援隊が来るかどうか（、あるいは水のあるところにたどり着けるかどうか）は全くわからない。それが問題である。」

(2)の文の冒頭に言葉を足すなら、「問題は」ではなく「手許｛てもと｝にあるのは」だと思う。
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