IQ scores become increasingly stable over time. Why might this be so?

Think about what a quotient means. If this is for individual scores, it's your estimated intellectual age compared to your physical age. As time passes and as more things are learned, our age (the denominator of the fraction) increases. It's like an average company. With more expansion come more expenses.

I am not sure this is an accurate statement. I say this because standard IQ scores are based on four main factors, and if you can increase even one of the factors, like working memory, you can increase your IQ score.

Because IQ measures your ability to 'learn/take in, process, and apply information, under time-pressure', the more often you do that, the better you get at it.