[Filligree]

We’re certainly not dying out. At minimum, eventually civilisation would crack badly enough that we can no longer make contraceptives, nor other entertainment to distract from sex.

Which I’m fairly sure is part of the picture. Evolution didn’t build us to want sex; it built us to crave stimulation, which is more generally useful, then made reproduction into fallback entertainment.

[newsy-combi]

Depends on what you mean by "we". Humanity? Yeah, impossible to die out by fertility crisis merely due to lifestyle. The fewer babies are born, the more unoccupied space there is, making it more and more attractive to have kids. But if you mean "Americans" or "ethnic population", it's very much possible to die out. It happened to native Americans, it can happen to your group. If birth control collapses in your country, you can still be supplied by another one from across the globe who secretly or openly cheers for your collapse. Same goes for shipping you drugs, see history. As for space becoming available from your low fertility, alas that doesn't work when you're being invaded and your land settled in by a more fertile country.