A comment has been deleted which referred to Capa's photography at D-Day, but as he is one of the more famous photographers of the time, let's start there. At the time of D-Day, Capa used a Contax II a "miniature" rangefinder camera similar to a Leica (which he had previously used). Miniature in this context means that it used 135 film (now colloquially known as 35mm) rather than the usual 120 film or 5x4 sheet which was more popular at the time. This would have allowed easier handling, and a greater depth of field. It also meant that reloading the camera in the field would be easy (possibly a reason why he stopped using Leica, which are notoriously fiddly to load).

The cameras of the day were considerably simpler than now, which helped with robustness. A war photographer would probably only use a 50mm prime lens which would remain on the camera. The lens had a simple diaphragm. but might have no other moving parts - for instance the Contax II was moved bodily by the camera rather than having any intrinsic means of focus. This was usually the case for larger cameras as well, although they might have a shutter in the lens.

A rangefinder has no reflex mirror, unlike today's DSLRs. There was a simple shutter at the rear, usually made of fabric.The shutter might go out of calibration, but with black and white film it would have to be a long way out before it would prevent you getting a shot.

Generally with a miniature camera, the photographer would leave the f stop at f/8 - as Weegee put it in the 40's "f/8 and be there". This gave a good depth of field, so that you could generally take a snap shot without focusing and get a reasonable result - also if your focus mechanism went down, it didn't stop you working. So basically the only thing that would stop you working would be a failure of the shutter mechanism. Probably just as well, as Leica and Zeiss were German-made and for some reason spares seemed to be difficult to locate in this period.

Just a note on a different camera of the period: the Graphlex Speed Graphic. This was the classic US press camera, and was also used for war photography. However as it was a 4x5 (or 5x4 in UK terminology) taking single sheets, it was not great for work on the front line and I'm not aware of anyone using it at D-Day. It was generally loaded with either a double-sided film-holder (i.e. two shots), or a device which could shuffle through six sheets separated by thin metal septa. A skilled photographer could work the camera fast even though absolutely everything was manual (e.g. you have to remember to cock the shutter yourself, because the camera will not do it for you). Murray Becker managed to get off all six shots between the Hindenburg catching fire and it hitting the ground, which shows you what was possible.

With a Speed Graphic, being able to carry on shooting depends on the camera having a minimum of two ways of doing anything. Two shutters for instance (usually) - one in the lens, and a focal plane shutter at the back. Aim it with a wire frame viewfinder, the glass viewfinder, or the ground glass plane. Focus it with the Kalman range finder, the scale, or the ground glass. Fire it with the front or rear trigger, or use the electric trigger on the flashgun to power a relay (before all the flash-guns were converted to light-sabres as Star Wars memorabilia). Due to the simple design, they were sometimes converted to take 70mm roll film (used for aerial photography in the period). Generally they were used with a 150mm lens, but making a new lens-board is quite simple and provided a way of recovering from front-end damage. It was quite common for them to be used with 28-40" "Big Bertha" lenses.

Journalists weren't the only individuals filming the war, as some soldiers brought along their own equipment. A good example of this is Robert Fuller, a Hollywood director who served as an infantry soldier with the 1st Infantry Division. Fuller carried an 8mm Bell & Howell camera with him while storming Omaha Beach on DDay; he earned a Silver Star on that day helping to open a hole on the German line, and when communications went down, making an insane dash across open sand to inform his commander. Fuller said he preferred the B&H because it was rugged and handled wet, cold conditions well. He filmed the Battle of the Bulge, and near the end of the war, the liberation of Falkenau Concentration Camp in Czechoslovakia. I saw portions of this film while doing research at Huntington Library, and it shows the citizens of the city next to the camp - man, woman, and child - being forced to walk through the camp and view the human carnage. He filmed as his unit forced locals to collect the dead bodies littering the camp, and give them proper burials that included a funeral procession.

Sources:
LIBERATING IMAGES? Samuel Fuller's Film of Falkenau Concentration Camp, Marsha Orgeron. Film Quarterly. Berkeley: Winter 2006/2007. Vol. 60, Iss. 2; pg. 38, 10 pgs

Fuller, Samuel, Christa L. Fuller, and Jerome H. Rudes. A Third Face: My Tale of Writing, Fighting, and Filmmaking. New York: Alfred A. Knoff, 2002.

I don't know if this info helped but you might also consider looking into George Stevens, another Hollywood director and cameraman who was assigned by the military to film the war. Like Fuller, he filmed DDay landings, but from a greater distance. He also filmed numerous concentration camp atrocities that were used during the Nuremberg trials; the footage was also placed in the Library of Congress. I'm sorry to say my notes don't tell me what camera he used.

Source:

Moss, Marilyn A. Giant: George Stevens, a Life on Film. Madison: University of Wisconsin Press, 2004.