Islam believes in God’s birth - Jesus Christ’s birth and his second coming. But why does Islam not believe in his death?

You said, “Islam believes in God’s birth.” No we don’t. [1]  We believe in Jesus’s birth. One of the basic attributes of God is that He is Eternal.[2]  Once we say that God is Eternal, to speak about His Birth, or His Death is contradictory.  He is without beginning, without end. Everything else of His Creation has a beginning and has an end. So we don’t speak of God’s Birth, nor do we speak of God’s Death. We speak of Jesus’s birth and we do not believe that Jesus was God.  Jesus, we believe, was a prophet of God. We do believe he was born of a virgin and that Mary was not married. So we do believe in the virgin birth. [3]

But the virgin birth was still, by the Will of God and an act of creation of God. We believe Eve was born without a mother. So if Jesus was God because he was born without a father then what do we say of Eve?  Furthermore, Adam came into being without a father and mother, so what do we say of Adam? [4] Therefore, we look at Jesus’s birth, although miraculous, as being a part of the four modes of creation. God may create us without a father and mother, or with father and mother, or without a father, or without a mother. These are the four possibilities.

References:

[1] “"He begets not, nor was He begotten” Quran 112: 3

[2] “Allah! La ilaha illa Huwa (none has the right to be worshipped but He), the Ever Living, the One Who sustains and protects all that exists” Quran 2:255

[3] “And (remember) she who guarded her chastity [Virgin Maryam (Mary)], We breathed into (the sleeves of) her (shirt or garment) [through Our Ruh - Jibrael (Gabriel)], and We made her and her son ['Iesa (Jesus)] a sign for Al-'Alamin (the mankind and jinns).” Quran 21:91

[4] “Verily, the likeness of 'Iesa (Jesus) before Allah is the likeness of Adam. He created him from dust, then (He) said to him: "Be!" - and he was.” Quran 3:59