Boiling water for too long does dramatically affect the quality of tea. The desirable brisk taste of tea is created by the interaction of two of its main components, caffeine and polyphenols. Each component is harsh on its own but as a complex the compounds moderate each other. Acid levels of water affect the behaviour of these components.
Water contains minerals and gases absorbed from the earth bed and air. Carbon dioxide absorbed by air makes the water slightly acidic that influence the colour and taste. High temperature changes the acidity of water and the acidity is reduced by gradually driving out carbon-dioxide. Therefore re-boiled water might well brew tea of a different colour and strength and is unsuitable to brew a good cup of tea.