Count the number of occurrences of a word
First of all, these interview questions are often a trick. It doesn't really matter if your code works for all cases (everybody makes mistakes). What does matter is how you write the code.

Even if they ask specifically for 'a' or 'A', you are not supposed to hardcode these values. They are a parameter. Understanding what is the input to your program is always the first task. If they ask you "Make a program that counts the number of times the letter 'a' occurs in 'Example'", the correct answer won't be return 1;. They also ask for words, you shouldn't assume that the program should search only for words withs 1 letter.

Second - words are not usually delimited only by a space. You should consider all whitespace and punctuation characters. Or just declare a function isWordDelimiter(char) and don't implement it.

Third - your code is not easily readable. An if inside another if in a for? Use functions. Example (pseudocode - I am not C++ programmer and I forgot STL):

while ((word = getNextWord(input)) != NULL) {
    if (word is in set of searched words) {  //replace this with STL set
        count++
    }
}

Summary:
Even on a very simple program, they can see how much experienced you are. Good developer won't just write something that works. He has to think how the problem will evolve in the future (different parameters), how the program will be maintained (write readable code). Good developers also write programs from top to bottom - first define the structure using high level functions, then write the implementation of the functions.