The bleaching action of Chlorine is permanent because it involves the process of oxidation. Chlorine reacts with water to produce nascent oxygen. This oxygen combines with the colours material and makes it colourless. It a powerful oxidising agent. Hence bleaching action of Chlorine is permanent The reaction involved here is:
Cl2 + H2O ——→ HCl + HClO
Hypochlorous acid is unstable, and it easily dissociates to form nascent oxygen.
HClO ——→ HCl + [O]
Colour material+ [O]⟶Colourless
The bleaching action of sulphur di oxide is temporary because it involves the process of reduction. sulphur di oxide removes oxygen from the coloured substance and makes it colourless. Atmospheric oxygen slowly takes place of the removed oxygen and because of which the material regains the colour.
The reaction involved here is:
Colour material+[H]⟶Colourless Colour (in presence of air)