EDIT: Quoting the unofficial Hacker News FAQ:
"You can only downvote comments once you have sufficient karma. The required level rises over time to account for the karma inflation caused by an increasing userbase.
If you do have enough karma to downvote then the reason might be that you are looking at a response to a comment of your own, or the comment may be older than 24 hours."
The quote you've provided is somewhat misleading, as the required level is not truly dynamic/automatic. It may "rise over time" but it is solely dependent on administrators/moderators manually raising the threshold.
As I said in the original post, the threshold should vary from user to user... not be a static, arbitrary number (currently 500) adjusted over time by administrators/moderators. Admins/mods should however tweak the algorithm that determines the threshold. And this threshold should change by the day, maybe even hour... even if only by a fraction of 1 karma point.