When we feel anxious, be it a brief sense of fear or a formal diagnosis of fear, that feeling stimulates the sympathetic nervous system, also known as the "fight or flight" mode. When we feel anxious, cortisol levels rise, the heart starts beating faster, and the rate of breathing increases.
Breath is only one aspect of fight or flight. Therefore, it is very common for people with anxiety to experience the inability to hold or slow their breath, or to become aware of that breath.
Fight or flight is a natural self-preservation technique and it actually means that the body is functioning properly. Our job is to find out what is causing this stress response and start doing it.