There is a story of von Rundstedt (C-in-C West) telling OKH to "make peace" shortly after the Normandy landings in June 1944. Mind, this was the same von Rundstedt who opposed the July 20 bomb plot to assassinate Hitler, so whether or not he really believed the war was lost or whether this view was shared by the Heer in general is up for debate.
Regardless, any well-trained general staff drilled in logistics and getting reports from the front after '43 would have been able to conclude that the War was not going Germany's way and it would only be a matter of time before the eventual end. That said, most of them saw their mission as one of drawing it out until the political leadership of Germany could secure favourable terms. It appears they never really considered that there was no political alternative to the Nazis except themselves, and that the Allies had limited appetite for anything but unconditional surrender.
Sources: The Last Prussian by Charles Messenger, and, IIRC, it was also reported the Desert Fox book on Rommel.
I'll suggest these as starting points, but not at all to discourage further discussion.
More questions, info, and debate are welcome, especially in this case. I think these replies are of use, but I'd love to see a big, comprehensive, and well-sourced answer.
"In World War II, when did Germany's commanders realize they were going to lose, and that the US was a major reason?" at https://www.reddit.com/r/AskHistorians/comments/7ta5c2/in_world_war_ii_when_did_germanys_commanders/ , answer by /u/Bodark43 .
"when did different levels of Germany know they were going to lose?" at https://www.reddit.com/r/AskHistorians/comments/7y7odg/when_did_different_levels_of_germany_know_they/ , answer by /u/IhitthedAb
This is a post that focuses more on the effects: "Why did Nazi Germany's Wehrmacht continue to fight even in the face of overwhelming defeat in late 1944-45?" at https://www.reddit.com/r/AskHistorians/comments/76z1m1/why_did_nazi_germanys_wehrmacht_continue_to_fight/ , answer by /u/GTFErinyes