I am afraid she will have this " bad mark" for ever now and something that she has to declare if and whenever she applys for any visa.
Even if she did appeal and win, it will not remove this mark. So if she was ever asked again, whether she has been refused a visa, she will have to declare it.
Lots of people get refused and then reapply fresh again and succeed.
Remember the refusal is based on the circumstances at the time the ECO makes the decision on the application. If you can not satisfy his doubts he will refuse you at the the time.
However if after 3 months your circumstances change and you can satisfactorily meet the regulation, then he would be reluctant to refuse you because of your previous refusal ( although they do look at previous reasons when deciding).