On Yom Kippur, Neilah represents the climax of the day. Hashem as it were, is about to seal our fate and finalise our year ahead. It is correspondingly a time to really storm the heavens and daven with a greater level of intensity.
The Mishnah Berurah 623:3 writes:
כי בנעילה הוא חתימת הגז"ד שנכתב בר"ה על בני אדם לטוב או לרע ויזדרז מאד בתפלה זו כי תכלית כל העשי"ת הוא יוה"כ ותכלית יוה"כ הוא תפלת נעילה שהכל הולך אחר החיתום ואם לא עכשיו אימתי ולכן אף אם חלש הוא מחמת התענית מ"מ יאזור כגבור חלציו להתפלל במחשבה זכה וברורה ולקבל ע"ע נדרי התשובה באמת והבא לטהר מסייעין אותו ויחתם בספר חיים טובים.
Because Neilah marks the sealing of our judgement that was written on Rosh Hashanah on every person whether for good or bad, he should be very zealous with this tefillah because the main point of all the Ten Days of Repentance is Yom Kippur, and the main purpose of Yom Kippur is Neilah since everything goes after the sealing, and if not now, when? And therefore, if a person is weak as a result of the fast, nevertheless, he should gird his loins like a mighty person to pray with a clear and meritorious thought and to receive the vows of repentance in truth and come to purify himself and be signed in a book of good life.
One of the kibbudim of this auspicious time is to receive pesicha from the beginning of chazaras hashatz (the Chazzan's repetition of the amidah) which has many a segulah attached. Indeed, many shuls bid money for the honour (refer to the Nitei Gavriel on YK - footnote 36).
Imagine though, that someone ahead of time is offered the honour but this person likes to take his time over his shemoneh esrei and tends to daven beyond the time that chazaras hashatz begins. Is it better for him to concentrate on his own amida where he can take his time with his kavanna and add all his personal bakashos (requests), or should he cut short his amida, i.e. do it in less time than he would normally so that he can do pesichas neilah?
