How did the Ministry of Propaganda fail to hide it from them?
It has been some time since I've read it so anyone should feel free to correct me on this. William L. Shirer in the rise and fall of the third reich writes that it was Britain's ability to bomb Berlin during daytime and nighttime raids that woke up Germans to the reality of war and the prospect of losing.
German anti-aircraft was unable to shoot them down because they had the ability to fly above the clouds. Of course, try as they might, the Nazi propaganda ministry couldn't hide the bombings from everyone and a defeatist mood eventually set in amongst some of the population.
I'd suggest reading Goebbels' annual addresses to the German population on Hitler's birthday. From 1939 to 1945, the tone shifts from triumphant to acknowledging that Germany is on the verge of defeat. They give an interesting insight into the official line on the progress of the war.