Using the same letters of Recommendation from previous admission cycle
You should always try to get newer, up-to-date letters, if the first set didn't work. 

You should try your best to get a letter specifically from the gap year, such as work experience or another type of academic program, that would benefit you greatly.

From personal experience, if it doesn't work the first time, trying again with the same package typically doesn't provide you a major benefit and ends up being you wasting money for admissions fees.