I have the following Python script that reads numbers and outputs an error if the input is not a number.
import fileinput
import sys
for line in (txt.strip()
Using the "for line in file:" form of reading lines from a file, Python uses a hidden read-ahead buffer (see http://docs.python.org/2.7/library/stdtypes.html#file-objects at the file.next function). First of all, this explains why a program that writes output when each input line is read displays no output until you press CTRL-D. Secondly, in order to give the user some control over the buffering, pressing CTRL-D flushes the input buffer to the application code. Pressing CTRL-D when the input buffer is empty is treated as EOF.
Tying this together answers the original question. After entering some input, the first ctrl-D (on a line by itself) flushes the input to the application code. Now that the buffer is empty, the second ctrl-D acts as End-of-File (EOF).
file.readline() does not exhibit this behavior.