Having the AirTurn function ON disables the keyboard pop-up window in Mail app.
Turn it OFF in iReal Pro under Settings/Airturn (or More/AirTurn in older versions of iReal Pro).

On older AirTurn devices, turn off your AirTurn to reveal the keyboard.
On newer AirTurn, just push the keyboard button on your AirTurn. Please see your AirTurn manual for more information.

If Airturn is ON and you have turned off Bluetooth on your device, you won't be able to turn Airturn off.
Temporarily turn on Bluetooth, then you will be able to turn Airturn off in iReal Pro.