Hello!
I took a look at the PMI PMP Exam handbook
www.pmi.org/-/media/pmi/documents/public...ssional-handbook.pdf
Page 31 states that "If you fail the examination three times within your one-year eligibility period, you must wait one year from the date of the last examination you took to reapply for the certification...... If your eligibility period expires without you passing the examination, you must reapply for the certification".
This would mean if your one-year application period is near expiring and you did not attempt the 3rd time, you can reapply for the certification again after the expiration date, and so you don't have to wait for another year (if you fail in your 3rd attempt). However, note the negative aspect of letting your application expires:
(1) you may be randomly selected for audit
(2) the exam fee will be more expensive than the re-exam fee
(3) you still have to wait for PMI's approval before you can schedule your next exam date (although this will give you more time to study).
As mentioned by Cornelius (the link you posted), this would be a personal choice since you have to take into consideration your time, work, family, etc.