My mother in law nearly did the same thing. Her birthday is mid November. If she retired on 11/1 vs 12/1, the difference in her monthly SSA check was going to be about $150 more. My father in law had already retied too early at 62, so he was getting a check that was nearly $300 less than hers, and they hadn't saved for retirement, so the plan was to live on their SSA income.
My mother in law was always bad at math, she just looked at $150 more as "not that much money". I had to point out that she was passing up nearly $2K/year for basically working an extra 3 weeks, since Thanksgiving week was only 2 days at her job. Eventually, she conceded and stayed on till 12/1.
Fast forward to a few weeks ago, where she had a sudden bout of illness and passed away, barely 2 years after retiring. :( My father in law has a tough road ahead, but at least he will be able to claim her SSA amount now, so that $150 extra/month has become incredibly valuable.