An AirTurn page turner reports itself to the device as a keyboard, and a device with a keyboard attached does not show the on-screen one. That is why the keyboard stops appearing when you tap a text field.
Two ways around it:
  • Tap in the text field, then press the keyboard button on the AirTurn itself to bring the on-screen keyboard up. Check your model's manual for where that button is.
  • Or turn AirTurn off in iReal Pro under Settings > AirTurn while you type, then turn it back on.