AirPlay link always down after few seconds

Indeed. Kodi does not support mirroring at all and never has. To make video playback work at all with iOS 8 it was necessary for Kodi to advertise to the iOS device that it does support mirroring when in fact it does not. (Otherwise the iOS device will refuse to see it as a video capable device and you will only get audio)

This causes the mirroring toggle to appear on the iOS device but you must not enable it or you will lose the connection and in fact you will find that the Airplay target will disappear and may not reappear for some time, making it difficult to reach the toggle to turn it back off again. (Sometimes a reboot of the iOS device is needed, then turn the toggle off again before attempting to connect)