Our international organization spells out in the NM manual that all NM and initiation fees are non-refundable, therefore if someone pays them, they're not getting them back.

as a local we have a contract the new members have to sign. if the new member decided to depledge before initiation, money will not be refunded. (That money goes toward their gifts on bid day, pins, etc so we kinda need it.) If they throw a fit, we show them the contract they signed. the end. :D

Our new member fees are non-refundable

Assuming she's telling the truth which there's probably no reason to doubt, her reasons are not 'I just don't feel it right now' or vague comments about 'stuff getting in the way' rather they are issues which were she an active in some sororities might lead to her petitioning the exec. committee or even nationals to go early alumna status for a period anyway?

The following comments are in the absence of any national rules you may have which say otherwise.

You stipulated she paid upfront a new member fee and initiation fee. I am guessing she has not been initiated yet, I would therefore refund that (poss. minus costs spent for her by sorority) since her present difficulties may be beyond her control. On the new member fee, it depends whether she has taken part in any new member activities which the new member fee was to cover or not - if she has a deduction could be made to cover those and balance refunded if not the balance minus an administration fee to cover all costs incurred could be refunded. All of this would in any event be discretionary.
I guess ultimately your sorority (I'm guessing from your posts which one it is) has waited over 70 years for her and if it needs to wait a little more until she can give it the attention and commitment she and you want to, then maybe that should be allowed and she not be disadvanted because her enthusiasm was there but other practical considerations got in the way.

But like I say a) echoing other comments check for existing policies or b) discretionary.

Our policy is that if you paid them, you paid them, non refundable. One thing that you could think about is that if she would like to join at a different time say within the next year maybe, then explain that her money wouldn't be wasted and she wouldn't have to pay again. Nationals will always clear the problem up though, they know all the answers!

It looks like the consensus is:

CALL NATIONALS! :)

Actually, I think a guy in a fraternity may join another national fraternity only if he petitions and gets released from the other. Correct me if I'm wrong, but thats what I've been told by some of the guys on my campus.

Though we are local we have a rule that the plege fee is non-refundable.