There is a timeout in the Serial.parseInt() function. Because the serial cannot be sure whether it received all digits of the integer or not. You can reduce the timeout with the Serial.setTimeout() function.
"Parsing stops when no characters have been read for a configurable time-out value, or a non-digit is read"
So you might be able to send a "stop" character a letter for instance.
You can find the description in the Arduino reference.