The sentence is correct, but a little odd with the word-order. "In which" and "that" introduce a relative clause, but "you did it" doesn't fit a relative clause (the problem word is "it" here). "If" doesn't fit because it's not a hypothetical situation - this is Paley's second mistake. "Paley, look at your paper. Why have you a second time made the same mistake when you did it a month ago?"

The sentence is correct. The correct answer is "when".

That whole sentence just doesn't sound right.

Thanks xarmanla, so, "when....." is an adverbial clause of condition?

There is an error in the question, but "when" is the answer based on the "did it". Apparently, she is supposed to remember the error she made. The "when you did it" may refer to "the mistake" so "the same mistake" is a problem. The other possibility is that on this day she made the error twice, but last month she got it right. In this case the "when you did it (correctly) a month ago.