EEA Nationals right to reside as student

Just wondering if anybody can see a legal challenge here.

Ct is french national and enrolled on course in the UK after arriving in the UK. She was self sufficient at the time because she was being supported by her partner, also an EEA national who worked and claimed WTC. The course of study was free. Ct has a 3 year old son who is not yet in full time education.

Ct separated from partner, while ct was still enrolled on course and she claimed HB/CTB. This was refused on the basis that she does not have right to reside for benefit purposes.
However, I am wondering if this can be challenged as ct was self sufficient when she started her course.

The issues I see with challenging this are:
1) Does, according to legislation, the ct need to be self sufficient for the full duration of her course or only at the beginning.
2) Can the ct be deemed to be receiving a service for the purposes of legislation, when the course of study was free (presumably paid for by UK state) and she enrolled on the course after entering the UK.