Final answer:
Magwitch is shamed by his criminal past and its implications for Pip, whom he secretly supported, and for this, he asks Pip's forgiveness in 'Great Expectations.'
Step-by-step explanation:
In Great Expectations, the one action for which Magwitch repeatedly asks Pip's pardon in chapters 40 and 42 is his criminal past and the fact that he, as Pip's secret benefactor, is a convict. Magwitch is deeply ashamed of his past actions and the stain his criminal history may cast upon Pip, whom he considers a gentleman. He is also remorseful for the social and personal implications his association may cause for Pip and sincerely asks for his pardon on multiple occasions.