The correct answer is A. litanies of and E. avid.

Here is a breakdown of the sentence:

The sentence sets up a cause-and-effect relationship. Newman's actions have exhausted the public's patience, leading even his most loyal supporters to turn away.
- Blank (i): The blank describes Newman's repeated criticism of the government. The phrase "had become so frequent" suggests a long, tedious repetition.
- A. litanies of: A litany is a long, tedious, or repetitive recital. This perfectly captures the sense of Newman's frequent, drawn-out criticisms.
- B. rebuttals of are arguments or pieces of evidence presented in opposition to something. While he may be rebutting, the word doesn't convey the sense of repetition and tedium.
- C. epiphanies are moments of sudden and striking realization. This does not fit the context of a repetitive act.
- Blank (ii): The blank describes the type of supporters who were shifting the dial. The word "even" suggests that these were the most devoted or dedicated supporters.
- E. avid: This means having or showing a keen interest in or enthusiasm for something. This word perfectly describes a supporter who is very dedicated to Newman.
- D. discerning means having or showing good judgment. While they might be discerning, the word doesn't directly imply loyalty.
- F. contentious means causing or likely to cause an argument. This describes the nature of his supporters, not their level of loyalty.

The completed sentence is: "The public only had so much patience with Newman: his litanies of the government's supposed ineptitude had become so frequent that even his most avid supporters soon began to shift the dial on their radios."