Let's break down the sentence to understand the context:
- "When my health began to $\qquad$ " - This indicates a change in the speaker's health.
- "...I started keeping a journal in which I chronicled my increasingly labored breathing and ever-present fatigue." - The symptoms described ("increasingly labored breathing and everpresent fatigue") clearly point to a worsening or decline in health. Therefore, the blank needs words that mean to decline, deteriorate, or become worse.

Let's evaluate the given options:
- A. degenerate: To decline or deteriorate physically, mentally, or morally. This perfectly fits the idea of health worsening.
- B. deride: To express contempt for; to ridicule. This word refers to mocking someone, not to a state of health.
- C. develop: To grow or progress. This is the opposite of what the symptoms suggest.
- D. diminish: To make or become less, smaller, or weaker. This also fits the idea of health declining or becoming weaker.
- E. distribute: To give out or spread. This word is unrelated to the state of health.
- F. daunt: To make someone feel intimidated or apprehensive. This word relates to fear or discouragement, not health.

Both degenerate and diminish accurately convey the meaning of health declining or worsening in the context of the described symptoms.