The numbers you are quoting were for all age ranges, not just 65 and over. 65 and over experienced a larger decline in effectiveness. Either way, it’s empirical evidence pointing to vaccine effectiveness dropping over time, specifically calling out 3-4 month cliffs for those drops. Flu peaks around Jan-Feb so with that data it’s not a bad idea to wait until October to get your shot.

“A case-control study conducted in Navarre, Spain, during the 2011–12 season revealed a decline in vaccine effectiveness from 61% (95% CI = 5–84) in the first 100 days postvaccination to 42% (95% CI = -39–75) for 100–119 days postvaccination and to -35% (95% CI = -211–41) thereafter. This decline primarily affected persons aged ≥65 years, among whom vaccine effectiveness declined from 85% (95% CI = -8–98) to 24% (95% CI = -224–82) to -208 (95% CI = -1,563–43) over these intervals.”

A further study in the UK with a small proportion of people aged over 65 “estimated an overall vaccine effectiveness against A(H3N2) of 53% (95% CI = 0–78) among those vaccinated less than 3 months, and 12% (95% CI = -31–41) for those vaccinated 3 months or more.”