Why do you think he has stopped writing to me?

As I think the structure of this whole question is important, and it would be good to have more explain.
Because first I thought the meaning of it: WHY do you think THAT the second part of the sentence is true?
But from the context I guessed the meaning is: WHAT is your opinion? WHY has he stopped writing to me?
You know, the combination of the two question is a bit strange for me.

Two different explanations:

(1) “do you think … ?” + “why has he stopped writing to me?”
The former phrase is inserted into the latter sentence.

(2) I think he has stopped writing to you because … <—> Why do you think he has stopped writing to me?
because . . . <—> Why
I think <—> do you think … ?
he has stopped writing to you <—> he has stopped writing to me

"WHY do you think THAT the second part of the sentence is true? " This is the correct interpretation.

  1. “Who do you think that man is?”

  2. “What do you think I have in my hand?”
    (Royal English Grammar with Complete Examples of Usage, p. 252)

  3. I think that man is [Mr. Smith]. (Mr. Smith —> Who, I think —> do you think … ?)

  4. I think you have [a diamond ring] in your hand. (a diamond ring —> What, I think —> do you think … ?, you have —> I have)

P.S.
Who/What/Why etc. do you suppose …?
What do you suppose he’s doing?
(LONGMAN English-Japanese Dictionary)

It is said that you should think about the possible answers to the question that you are going to construct.

@kimojima
I think that the title sentence is not the poster’s question. He or she is interested in the structure of the sentence.

"Because first I thought the meaning of it: WHY do you think THAT the second part of the sentence is true? " I think that this “why” in the title sentence is related to the reason of someone’s behavior or non-behavior in this case.

Two possible answers:

  1. I think he forget about you.
  2. I think so because I know you have received no replies from him.

I wonder which Is right. Which kind of answer is in the mind of the person who posted the question?

I am sorry i did not write it. This question is a quote from the “Who is She?” story Part 6. (And the "Who is She?, Focus on vocabulary Part 6., where Jill and Steve are discussing about the sentence, and they do not say anything about the combination of the two questions)

What do you think …?
believe, consider, expect, fear, guess, hope, imagine, say, suggest, suppose, think, tell.

Do you know what …?
explain, know, remember, understand
(The Royal English Grammar for Practical Expressions, p. 221)