When a person is sick his immune system is compromised and his physical wear and tear is increased. Is this analogous to a more disordered state as evidenced by an increase in entropy?

That is why terminal illness precipitates death faster. Please advise.

It is a matter of how people define the terms. When you are well, you are in a far-from-equilibrium state, your functional complexity and information content are high and entropy is also high. When you are ill, there is a state of reduced functional (but sometimes increased structural) complexity, energy loss continues to be high until it slows down to eventually zero, a point of (physical, but not biological) equilibrium and maximum predictability i.e death.