に限って details

にかぎって

of all times/people — ironic bad luck; also, "of all people, X would never"

今日きょうに限かぎって傘かさ持もってくるの忘わすれたよ。

kyou ni kagitte kasa motte kuru no wasureta yo.

Of all days, I forgot to bring my umbrella today. casual

あの真面目まじめな田中たなかさんに限かぎって、遅刻ちこくするはずがない。

ano majime na tanaka-san ni kagitte, chikoku suru hazu ga nai.

Of all people, someone as conscientious as Tanaka would never be late. neutral

Examples

of all times/people — ironically, the worst possible moment turns out to be exactly when something (usually undesirable) happens

今日きょうに限かぎって傘かさ持もってくるの忘わすれたよ。

kyou ni kagitte kasa motte kuru no wasureta yo.

Of all days, I forgot to bring my umbrella today. casual

急いそいでいる時ときに限かぎって、電車でんしゃが遅おくれる。

isoide iru toki ni kagitte, densha ga okureru.

Wouldn't you know it, the train runs late exactly when I'm in a hurry. neutral

に限って〜ない — of all people, X would never; a categorical, trust-based denial

あの真面目まじめな田中たなかさんに限かぎって、遅刻ちこくするはずがない。

ano majime na tanaka-san ni kagitte, chikoku suru hazu ga nai.

Of all people, someone as conscientious as Tanaka would never be late. neutral

弊社へいしゃの社員しゃいんに限かぎって、そのような不正ふせいを行おこなうことはございません。

heisha no shain ni kagitte, sono you na fusei o okonau koto wa gozaimasen.

None of our employees, of all people, would ever engage in that kind of misconduct. formal

はずがない
はずがない reasons from evidence to a flat "shouldn't be possible"; に限って supplies the reason for trusting this particular person or moment in the first place — あの人に限ってそんなことをするはずがない stacks the two, に限って naming who deserves the benefit of the doubt and はずがない delivering the verdict.

限り
限って singles out exactly one item and always carries an evaluative charge — bad luck, or absolute trust; 限り just states a plain boundary condition with no judgment attached, so 忙いそがしい時ときに限って sighs where 生いきている限かぎり merely reports.
に限らず
Same に限 root, opposite direction on identical morphology — に限らず widens a scope past N ("not just N"), while に限って narrows straight down to N, usually with an ironic sting ("of all things, N").
に限る
Both narrow the claim down to exactly one item, but に限る rates that item as the objectively BEST choice on offer, while に限って rates it as the WORST-timed coincidence (or the one person too trustworthy to doubt) — same narrowing move, opposite evaluation.