A 2001 paper by a Unilever Research team from Bedford, England, found that anything from growing conditions to the age of leaves, plant cultivars and methods of cultivation affects tea's caffeine content. All these things remaining equal, the temperature of water, leaves to water ratio and steeping times also have a big impact on caffeine in the end brew.
When it comes to steeping times specifically, it is true that a lot of the caffeine content is extracted in the first thirty seconds. As the brew time increases, the rate at which caffeine is extracted from the leaves slows down-but that's doesn't mean that the longer leaves are steeped, the less caffeine content the brew will have. In fact, it's quite the opposite.
According to this study, 34.6% of caffeine is extracted from the average teabag in the first 30 seconds of infusion. This figure will go up to just over 50% after a minute. After 5 minutes, the total caffeine extracted from the leaves will have gone up to more than 90%. By contrast, polyphenols are extracted more slowly, with just 19.9% extracted in the first 30 seconds. So the longer you steep your tea, the lower you push the rate of caffeine extraction per second and the ratio of caffeine to polyphenols--but the overall amount of caffeine will go up. Of course, if you are discarding the first infusion, the subsequent brews will have less caffeine and comparatively more polyphenols. Although the study looked specifically at teabags, I believe they said its results could be extended to loose leaves too.
The Linus Pauling Institute
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has a quick overview of caffeine in tea with links to the abstracts of a number of studies, if anyone is interested.