I assume the emulator cannot connect to the debugger for some reason. When I restart Android Studio logcat reports, but when I close the app running on the emulator it stops reporting. This CANNOT be the default intentional behaviour, does this affect other people? Many thanks for any help at all.
An answer to this part is that it does not sound like expected behavior of Android Studio / logcat / emulator. I am able to start and quit the app multiple times, each time logcat connects when the app begins and disconnects after. I can start the application through Android Studio or through the apps menu on the emulator. I can quit and restart the emulator.
An easy thing is double check the dropdowns along the top of the logcat display, especially the emulator, app, and filter selectors.
I once had an issue that sounded similar, with logcat not reconnecting. The issue there was my terminal and IDE were running different ADK installs and they were competing for the logcat connection. So what you describe is possible, but not the norm. Perhaps another debuggable app or connected device could cause similar confusion.