I've studied infertility and found that its quite complex to define. However, I came to know about a useful working definition of infertility; which was " Failure to achieve pregnancy". Few days later I've hit upon a idea that proves that definition wrong. As I studied the turner syndrome, in which condition was XO but individual was infertile female. Further I studied that if they are subsequently treated with Gonadotrophin hormones, they have menstrual periods as well. There I found that if a fertilized egg is implanted in their uterus, pregnancy would be achieved. Now how would we call that female infertile?
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.