Thanks for your question.
When you read 1 Samuel chapters 9 through 31 it becomes clear why Saul was not restored. He never repented. He declared his understanding of his error more than once but he never did anything to rectify the situation but persisted in his reckless commitment to doing things is own way even at the expense of the nation and in violation of God's direct commandment. David sinned grievously but was restored and forgiven as was the son of Hezekiah, Manasseh, who sinned horribly but he sincerely repented and was restored to the throne. Saul never did that. In fact, knowing what God required of him, he desperately sought to thwart God's will. If Saul had repented from his many acts of folly and had voluntarily stepped down [in the spirit of his son, Jonathan, who acknowledged David as God's chosen king and gave up his right to the throne], he would have not only been forgiven but he would have been held up forever as a wonderful example of faith and repentance. He never did that. He suffered the consequences. God is not an "avenging God" but he will not tolerate deliberate and continued disobedience.
God is a God of love. He is patient and kind but deliberate, premeditated wickedness has its price. Cain discovered that to his dismay as did those in Noah's day and Sodom and Gomorrah. The people of Canaan in the time of Abraham were full of vile evil. Abraham and his descendants were promised that land but could not have it until the iniquity of the inhabitants of the land was "full" and that took 400 years. God was desperately hoping for revival and repentance but there came a time when His patience came to an end. It came to an end just as it will for our world when Jesus returns.
Ezekiel 33:11 As I live, declares the Lord GOD, I have no pleasure in the death of the wicked, but that the wicked turn from his way and live;
If you want to come to grips with what the Bible really teaches, why not take the free online Bible study course available on our website,www.thisisyourbible.com? This course will give you a background in the major themes of the Bible from Genesis to Revelation. As with everything we offer, there is no cost to you other than your time and effort. You will also have a personal tutor to whom you may pose questions either from the course itself or those questions which come to you as you read the Bible.
I hope you have found this helpful.