Dragons have a special gland which generates the breath weapon
According to the D&D 3rd edition sourcebook Draconomicon (2003), chapter 1, a true dragon's breath weapon is produced by an organ in the chest known as the draconis fundamentum.
The draconis fundamentum (7) is a gland possessed only by true dragons. Attached to the heart, it is the center of elemental activity inside the dragon's body. All blood flowing from the heart passes through this organ before going to the body. The draconis fundamentum charges the lungs with power for a dragon's breath weapon and also plays a major role in the dragon's highly efficient metabolism, which converts the vast majority of whatever the creature consumes into usable energy.
The dragon converts energy taken from its diet into the breath weapon by means of this organ, which generates the breath weapon deep inside the dragon's lungs. The dragon must first inhale deeply, and then, if sufficient energy is available, it can exhale and produce the breath weapon.
D&D 3e asserts that a dragon's breath weapon is supernatural, and won't function in an antimagic field or similar. D&D 5e's FAQ v2.3 p.17-18 disagrees, saying that while dragons are innately magical, the breath weapon is merely part of the background magic that is part of the physiology of many D&D creatures. Either way, however, both editions agree that there's something magical about the dragon's physiology.
Given this lore, there are plenty of reasons why a dragon might be unable to use its breath weapon. Ecological disaster or overcompetition from a high concentration of other dragons in this area might make it difficult for the dragon to feed sufficiently to get the energy for its breath weapon. An illness might make its lungs or draconis fundamentum fail to work properly.
A very Dark Souls explanation might be that most of the the remaining dragons in this world are merely lesser dragons, a mere distant relative of the original true dragons, and as a result they lack the draconis fundamentum necessary to use a breath weapon; according to Draconomicon, this distinction also occurs in D&D between dragons and the other dragon-type creatures like drakes.