Psa 103:12 As far as the east is from the west, so far hath he removed our transgressions from us.
Heb 10:17 And their sins and iniquities will I remember no more.
Although God is seen in the New Testament as being a cruel and an unforgiving God. Many were his acts of forgiveness toward the Jews in the Old Testament, although they had followed other gods and mixed with other peoples in their environs.
With the formation of the New Testament period the promise of God in the flesh had manifested itself, which now opened the door for all persons to approach God in prayer without having to go to the altar to sacrifice doves and cattle to receive remission of sins.
Micah 7:19 He will turn again, he will have compassion upon us; he will subdue our iniquities; and thou wilt cast all their sins into the depths of the sea.
Isa 38:17 Behold, for peace I had great bitterness: but thou hast in love to my soul delivered it from the pit of corruption: for thou hast cast all my sins behind thy back.
1Jn 1:9 If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness.
The bible therefore speaks clearly on whether or not God forgive sins forever, and it is clear from the verses mentioned that God does indeed forgive sins forever.