That some of the trooper's Springfield trap door rifles jammed at the Little Big Horn is not denied but how much it happened and the effect on the battle is controversial and not to be taken for granted. Yes, there is evidence of jamming on some cases gleaned from the battlefield but there's no indication of many jams there were as nobody lived to tell about it. And some jammed on Reno Hill but were cleared easily enough and the defense of the hill wasn't threatened by it. Note too the trap door gave fine service at the Wagon Box and Hayfield fights. And when the cartridges were improved with better metal the extraction problem was pretty much fixed.
The British Martini-Henry was quite reliable in South African conditions and the defenders of Rorke's Drift, who fired their rifles so much they became to hot to hold, were well satisfied with the rifles, as 125 men who fired 20,000 rounds fighting off 5000 men might well be. At Isandlwana the British lost because they were poorly placed on the battlefield: the infantry companies were pushed too far out and were unable to support each other. The book "The Washing of the Spears" gave rise to the once popular notion that the Brits were overrun when their ready ammunition supply on the firing line ran out and more ammunition couldn't be run out to the lines because of logistical failures such as an inability to open the wooden cases in which the ammunition was stored. This notion is now not taken for granted and many consider it debunked. And as Pickett might have said: the Zulus had something to do with it.
Finally note that the Martini gave excellent service in subsequent battles of the Zulu War such as Ulundi and Ginginilovu (Sp?).
Martinis were prone to extraction problems in the sandy conditions of the Sudan. This was fixed when the rolled foil cartridge cases were replaced with improved drawn ones.