If it were a formal FWR then no this is not a legitimate reason for refusal

You are best to go back to partners and work through one of the legitimate reasons if there is one

...reference Flexible Working reasons for refusal 

Also let them know that FWR that are granted specifically don't set a precedent. The legislation is clear that the fact that a FW arrangement is in place may impact the ability of the organisation to grant another, and that consistency is not a requirement. Obviously, bearing in mind general principles of discrimination, and the obvious morale impact of granting the same flexible working arrangement to person B just after person A has been turned down for the same request.

Although all the previous answers are correct with respect to the legitimate grounds for refusal and that "setting precedent" both isn't one and also doesn't matter, I would also observe that this specific request doesn't fall within the definitions of flexible working as set out in the regulations. So the request itself wouldn't be valid under FWR and the lack of a legitimate rejection reason wouldn't render the decision itself unsafe.

What she has actually done is ask for a period of unpaid absence or, perhaps more accurately, for a temporary reduction in her contractual working hours (although I suspect she may not have considered the by-products of such a request other than reduced pay).

Neither of these things is a form of flexible working, which would require her to be asking for a permanent reduction in her contractual hours to qualify.

That said, it sounds like the partners could afford to be reminded on the importance of consulting a specialist before making decisions outside their field of expertise. It's amazing how often lawyers, of all people, seem to need to be reminded of this.