According to numerous postings here and elsewhere, it is not possible to record audio using the PlayAndRecord category while doing playback through airplay (from the same or another app).
However, this posting suggests it should be doable using Audio Queue Services as done in Apple's SpeakHere demo. It seems to improve matters, at least at first sight. But after 60 seconds of successful concurrent recording and airplay playback, airplay stops and playback continues on the device.
So my question is: Have anybody in fact ever succeeded in continuous, concurrent recording and playback through airplay for more than 60 seconds? In any way, not necessarily as suggested here. The author of the Audio Queue recommendation above (@glenstorey) is more than welcome to elaborate a little on how he succeeded - this entire posting was intended as a comment to his posting, but I do not have enough points to add a comment.