Huge thanks to Steve French for this one
Like him, I’d been having issues with “Edit and Continue” not working for ages. I tried everything and none of the usual advice helped at all. Finally I came across Steve’s post here, and as he suggests, uninstalling Stackify Prefix immediately fixed the problem. Turns out everything was fine to start with, it was just Prefix that was getting in the way (probably due to the way it injects itself into the runtime / server / etc).
For reference other settings I tried included:
Tools -> Options -> Debugging -> Enable Edit and Continue
Project Properties -> Web -> Enable Edit and Continue
It kind of sucks because I really liked Prefix, but it’s only useful in specific situations, whereas Edit and Continue is much more useful. I guess I’ll have to find another profiler…