I may be missing something on a larger scale, but that is definitely true about all poor people i know (for almost all of them, i see an easy way how they can quit poverty in a few years, apart from a couple very sad examples), and every rich person i know, too (while again, it may be just my perspective: i don't come from a rich family so i don't know anyone who was born rich).
It doesn't work as easy for older poor people. Sad for them, but it is only a result of their mistakes in younger age.
You may be mistaking cause and effect. Many poor people have grown up with such a dire outlook that instant gratification is all that's essentially worthwhile.
but it is only a result of their mistakes in younger age
This is just uncharitable Ayn Rand style sophistry. Environment and simple luck has a fantastically large multiplier on one's odds of being poor or not.
Luck is a factor but often I have met people (I grew up poor) whom don't play the odds in a rational way. For example a lottery ticket has a very low chance of paying off and yet many poor people play, those same people can't find the time or resources to submit a healthy number of resumes or job applications each week even though the odds of finding a better paying job (and one that can potentially lead to an even better paying job in a few years) is statistically speaking vastly more likely. My point being its luck to pick the correct number in a game of roulette but its up to you how many times you attempt to spin the wheel.
So, nothing happens in your world to drive older people into poverty though no fault of their own? It all has to be because of what they did? No financial crises, stock market crashes, stolen pensions, healthcare related bankruptcies, etc?
It doesn't work as easy for older poor people. Sad for them, but it is only a result of their mistakes in younger age.