"I am not crying."
Or maybe I did not understand the question? If the " was meant to represent a pause in speaking, then the answer would be "kinda yes, but...". I do think it is common that the い sound to be spoken softly and quickly, thus giving the appearance that there is no い. As far as what I've heard speakers in the Tokyo/Chiba area say, the い sound ,although very quiet, is still there.