Actually, tea doesn't really have true tannin in it. Rather, the astringency in tea is due to catechins and various other flavonoids. Both catechins and tannins are polyphenolic compounds, but are otherwise chemically unique.
As far as the exact chemical reasons for why tea tastes very bitter after a long steep, I do not know. However, the question has piqued me enough to research it out. Thanks!
In the mean time, you can add some auditory ambiance to your ruined cup by listening to The Fiery Furnaces' 2006 album, Bitter Tea.