What is working definition for female infertility?
Infertility is defined as the inability to conceive after one year or longer of intercourse without the use of contraception or therapeutic donor artificial insemination. 


That definition does not include a state of permanence.  That is, with treatment, fertility can indeed be achieved in many cases. 


  You may want to consider the term sterility as a definition, which has a permanence to it. But even then, if you consider tubal ligation (female sterilization) or a vasectomy (male sterilization), then you'll quickly conclude that sterilization can be reversed.  At that rate, you may want to state "irreversible sterility" where a genetic basis cannot be overcome with treatment/intervention.  Even then definitions may vary.


As you've discovered, even some genetic-based infertility can be overcome with IVF.  In terms of your genetic interests, the condition of XX male syndrome, resulting from loss of the SRY gene during crossover, causes the inability to produce any sperm (azoospermia).  There is no existing treatment for that or even a reasonable theoretical one. 

This could get more complicated/interesting as new medical therapies mature.  If one were to clone a human for example, is that a type of reproduction? Likewise, there is gene therapy, which could overcome some types of genetic-based sterility.

Sources:


http://medical-dictionary.thefreedictionary.com/Infertility
http://medical-dictionary.thefreedictionary.com/sterility
http://www.acog.org/~/media/For%20Patients/faq011.pdf