Should I grant an extension on an extension?
This would, to me, seem to depend not on dates and length of delay, but on the reasons behind them. I can easily see deciding in either direction, based on what the student gives for an explanation. 

Everything may be perfectly explainable, including not sending emails. Or you could decide that the student was just slacking. But base your decision on the reasons, as best you can determine them, not just the time factor.