Dr. Rank was not in a position financially when Nora needed the money to have helped her. Here is the text from the play that covers this topic:
Nora. I don't understand you at all.
Mrs. Linde. Don't prevaricate, Nora. Do you suppose I don't guess who lent you the two hundred and fifty pounds.
Nora. Are you out of your senses? How can you think of such a thing! A friend of ours, who comes here every day! Do you realise what a horribly painful position that would be?
Mrs. Linde. Then it really isn't he?
Nora. No, certainly not. It would never have entered into my head for a moment. Besides, he had no money to lend then; he came into his money afterwards.
Mrs. Linde. Well, I think that was lucky for you, my dear Nora.
Nora. No, it would never have come into my head to ask Doctor Rank. Although I am quite sure that if I had asked him--
Mrs. Linde. But of course you won't.
Nora. Of course not. I have no reason to think it could possibly be necessary. But I am quite sure that if I told Doctor Rank--
Mrs. Linde. Behind your husband's back?
Even though Dr. Rank was not then a "man of means", his obvious affection for Nora and attraction to her would have brought him to find the money for her, had she asked; perhaps, to have taken a loan himself, and then presented Nora with the money, eliminating the fraud. Nora, however, as seen above, would not have considered borrowing from a friend. It would have ruined her sense of independence gained from seeking out a third party.