It varies a lot. During one of the big thrice-yearly compos, your posts will fall off the main page within minutes (but there are tons of people reading), between compos a post might stay on the front page for a few days (but no one is checking the site). During the other events like a Mini-LD and the Oct. challenge it's somewhere in between.
Since anyone can write a post, is it hard to get your post seen? (Not sure how many new posts get written per day)