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Initial searching in Japanese-Japanese dictionaries seem to suggest that it's
along the lines of "has a bit of ..., so saying otherwise would be wrong",
"more so than not", and is a synonym to ないわけではない (though I personally don't
really understand ないわけではない either).

Am I understanding it correctly? What would be an accurate and/or good way
(these might not be the same) to translate it to English when it's part of a
sentence, or is it something that's heavily context-dependent? Would it be
something like "it's not that [negative clause]"?

While I do have a [specific example](http://sai-zen-
sen.jp/comics/twi4/tomochan/works/0294.jpg) of it being used that I'm
interested in, I'm also interested in the general case.

P.S., A fan translation of that example translated it as "Unfortunately yes".
Is this a good translation? Does the expression itself convey the
exasperation, or is it simply in the tone it's said?
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translation expressions particle-は negation
What does ...なくはない mean?
As far as I'm aware, なくはない is a double negative with the meaning being
something like, "it's not that (whatever was said) is not the case" with the
implication "(whatever was said) may be true, but there is some issue with
plainly stating 'yes.'" So I guess "not no" is a good way to think about it.

I personally wouldn't have translated that as "unfortunately, yes." I might
have gone with something like, "it's not like he can't do it." In this case
she happens to be exasperated because of her relationship with the character
in question (I happen to have read this manga), but the phrase isn't
specifically tailored for exasperation.
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わけではない is used when you're in a situation, or in regards to something that
someone else has said, to indicate the belief that although something might
seem to be the case, this may not hold true; however, it often can, depending
on the context, be used by speakers to simply deny things in a less direct
(euphemistic or roundabout) way to try to address the face needs of the
interlocutor. For example, in a sentence like "金がすべてというわけではない"/"Money isn`t
everything.", it's clear that the speaker is denying the statement. (There are
more examples at
[jgram](http://www.jgram.org/pages/viewOne.php?tagE=wakedehanai)).

The strength of the negation can be increased by using "別に" e.g. as in
"別に病んでるわけではない". わけではない can also be used to mean that something has some truth,
but is not binary.

It means "may not necessarily be the case that it's not...": the 訳{わけ} in
わけではない refers to something _meaning_ something, being the _case_ that, being
the _circumstances_ that ... etc.

* * *

However, with なくはない, my dictionary says that it means 全くないわけではない ("not like
it's entirely not") and that it also implies something can occur/take place,
so I believe it isn't quite a synonym of ないわけではない. I haven't seen this as much
as （ない）わけではない, but the
[実用日本語表現辞典](http://www.weblio.jp/content/%E3%81%AA%E3%81%8F%E3%81%AF%E3%81%AA%E3%81%84)
says that it tends to more often be used in a way which has negative
connotations, even if it doesn't necessarily convey exasperation.
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answer