Why did Oliver Cromwell's overthrow of the monarchy failed to win the support of the English people?

Because he was a religious zealot who banned theatre, musical performances and general celebrations (christmas as a feast day, for example). People wanted to be able to have fun, on a simple level.

On a more complex level, he was a tyrant. There were numerous factions involved in the revolution (Levelers and Diggers, for example), but once he declared himself Lord Protector he quashed them and ruled as a dictator. England did not prosper under Cromwell. He had no allies on the international sphere, and science and the arts were suppressed. Had he handled things better and actually given people what they wanted (land reform, a bigger say in governance etc.) then we never would have brought Charles II out of exile in France and reinstated the monarchy