Even a single female would be lost. There would be no repopulating the Earth. The gene pool would simply be far too small. This has already been established long ago, that you really need a minimum of a few dozen breeding pairs minimum to sustain a species.
And even that is pushing it to the absolute limit.
The sperm bank idea is a nice one but ultimately it would fail. Maybe she would be able to impregnate herself a few times that way, it would ultimately fail. Because the refrigeration would not last. She can’t maintain a power grid to keep refrigeration going on all sperm banks. No single human could do that.
And so, any daughters she would have… would not have sperm banks to rely on. By the time they were of child bearing age, there simply would be no more viable sperm banks.
And, well… breeding with their own brothers (assuming the woman really managed to birth quite a few children) would be a wash as well. Incest is not only ethically and morally objectionable, it is biologically speaking highly undesirable. Degeneration of the genome leads to all sorts of problems.
So, the gender point is mostly moot. A single human surviving would still lead to extinction of the species.
Well, maybe there’s one way… a single woman that managed to raid a few sperm banks, somehow managed to set up temporary mobile refrigeration and then moved to Antarctica. To use the natural refrigeration there. Still… unlikely it would work.