The answer depends on many things, including the state you are talking about and the service you mean and the result you want. Certainly, there could very well be some consequences for the error. But, simple errors (other than deadlines) are rarely the cause of major consequences. I find it unlikely a default judgment would not be reopened on a motion simply because the other side did not respond to a fax they never got, even though it was from their own error. On the other hand, if they claim you did not fax them something in a timely manner because of the error, it is hardly likely you would suffer a consequence.
But, don't take this as a tap-tap no problem forever. Notify the other side of the error and continue down the road in a responsible manner.