There is an underlying buffer/stream that getchar() and friends read from. When you enter text, the text is stored in a buffer somewhere. getchar() can stream through it one character at a time. Each read returns the next character until it reaches the end of the buffer. The reason it's not asking you for subsequent characters is that it can fetch the next one from the buffer.
If you run your script and type directly into it, it will continue to prompt you for input until you press CTRL+D (end of file). If you call it like ./program < myInput where myInput is a text file with some data, it will get the EOF when it reaches the end of the input. EOF isn't a character that exists in the stream, but a sentinel value to indicate when the end of the input has been reached.
As an extra warning, I believe getchar() will also return EOF if it encounters an error, so you'll want to check ferror(). Example below (not tested, but you get the idea).
main() {
int c;
do {
c = getchar();
if (c == EOF && ferror()) {
perror("getchar");
}
else {
putchar(c);
}
}
while(c != EOF);
}