A well system includes a fiber-optic cable positionable downhole along a length of a wellbore. The well system further includes an opto-electrical interface to communicatively couple to the fiber-optic cable to monitor a gas released from a well element within the wellbore. Further, the well system includes a processing device and a memory device that includes instructions executable by the processing device. The instructions cause the processing device to detect hydrogen absorption by the fiber-optic cable within the wellbore and determining a location of deterioration of the well element using the detected hydrogen absorption by the fiber-optic cable.