What ends the struggle between Satan and Death in Book II of Paradise Lost?
The struggle between Satan and Death seems about to come to a terrifically violent conclusion until Sin (the daughter of Satan and mother of Death) abruptly intervenes. She exclaims,
O father, what intends thy hand . . .
Against thy only son? What fury O son,
Possesses thee to bend that mortal dart
Against thy father’s head? (2.727-30)
Her sudden intervention astonishes Satan, who had initially failed to recognize his daughter and who, in fact, even now proceeds to insult her by calling her a “detestable” sight (2.745). (Later, of course, he flatters her, in his typically hypocritical way, by calling her his “Dear daughter,” just as he also hypocritically calls Death his “fair son” [2.817-18]. This abrupt change of rhetoric is just one of the ways in which Milton depicts Satan as a manipulator while also mocking him and making implicit fun of him.)
Only after Sin explains to Satan that she is the daughter whom he raped (thus producing Death) does the conflict between Satan and Death really end. Only when Satan realizes that Sin and Death can help him in his struggle against God does he adopt them as useful allies. Milton cleverly depicts Satan, Sin, and Death as a kind of unholy trinity, contrasting them with the holy trinity of God the Father, the Son, and the Holy Ghost.
The struggle between Satan and Death ends because it is mutually advantageous to all three members of the unholy trinity for it to conclude. Certainly it does not end because of any true wisdom or virtue on the part of any of those three. It ends because all three see ways to benefit from a convenient cessation of hostility
For an excellent brief overview of the poem, please see C. S. Lewis, A Preface to Paradise Lost (Oxford: Oxford University Press, 1961).