why is sulphuric acid not a drying agent for hydrogen sulphide?

A gas can be dried using sulphuric acid if the gas has no chemical action with acid or it does react with sulphuric acid.

Hydrogen sulphide gas cannot be dried using sulphuric acid as H₂S gas is oxidised by sulphuric acid to Sulphur. Therefore, the H₂S gas has chemical action with acid and hence it reacts with it , therefore, cannot be dried using it.

H₂SO₄ + H₂S -------> 2H₂O + SO₂ + S