My question is geared toward Math PhD programs, but perhaps I will broaden it a bit, so it serve useful for future questions. Hypothetically, if you applied to a graduate program and didn't get in a given admission cycle, is it viewed negatively by the admission committee if you applied to the same institution with the same letter writers next year of the 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.