It sounds to me like your sister is really anxious about her own life and since she can't control it (her son) is taking it out on you since she has the leverage of you owing her the money.

Do a lot of smiling sweetly and wishing her well :-) When you "agree" with someone they can't keep complaining for long. Figure out a list of "agreeable" phrases that are (in a way :-) true and e-mail them back when she gets in the e-mail mood. Things like, "Yes, I really feel horrible I wasn't able to pay you back yet" or, "I wish I could work more hours at this job" (nevermind why you don't :-) She won't get anything out of complaining to/about you and will have to find another victim.