Thanks for all your suggestions. I have gone with adding an event handler to the System File Task container and setting propagate errors to false.

It turned out that a part of the MDX code inside the cube was causing an error 
CREATE DYNAMIC SET CURRENTCUBE.[GNR and PI]
AS {[Lines].[Class POS].&[GNR],[Lines].[Class POS].&[PI],[Lines].[Class POS].&[GEN],
[Lines].[Class POS].[All].[Class POS Total]}, DISPLAY_FOLDER = 'POS Class...

It turned out that a part of the MDX code inside the cube was causing an error 
CREATE DYNAMIC SET CURRENTCUBE.[GNR and PI]
AS {[Lines].[Class POS].&[GNR],[Lines].[Class...