getchar() does not read EOF when not following ENTER

Question

I need to read the following format of text:

text
textEOF

Where EOF is a single CTRL+D and the rest are just the characters (\n is important).

The only way it does work is by adding another EOF after the first one, which I cannot do.

text
textEOFEOF

So I tried to use getchar(), but it seems to malfunction in some way or I am using it incorrectly. This is my code. What am I missing here?

    string a;
    int current;

    do {
        current = getchar();
        if(current != EOF) a.push_back((char)current);
    } while ( current != EOF );

    cout << a;