Breakpoints Not Hit in Azure Function
There is apparently a problem with how ConEMU takes over Window's opening of default console windows in this situation (you can read about this feature of ConEMU at https://conemu.github.io/en/DefaultTerminal.html).
Disabling this ConEMU feature -- which lets VS open a normal Windows console -- solved the problem; breakpoints were hit as per normal, without having to attach to the console running the Azure Functions local host manually. Of course, that means I lose the value of ConEMU shells opening within VS, but I can live with that. I will report the problem to the ConEMU team.
I did not have ConEMU but I had the same problem - function breakpoints had just stopped working. Furthermore the function runtime console didn't close when I stopped the process, it had done so earlier. Running in Visual Studio.
The solution was rather unintuitive: go to "Tools -> Options -> Debugging" and uncheck "Automatically close the console when debugging stops". After that breakpoints started working again even if the window still doesn't close automatically.