Why does it say "Netzach Yisrael"?
Rashi: Hashem, who is the Eternity of Yisrael, will not falsify (fail) to give good to the one to whom He said that He will give.
Targum Yonasan: If you will say, I will repent and I and my sons will reign over Yisrael forever - it was already decreed on you in front of the Master, the Eternity of Yisrael, that there is no falsity in front of Him, and He does not retract from what He says?
Me'iri: Based on Moshe's Tefilah "v'Niflinu? mi'Kol ha'Am" (Shemos 33:16. Regarding Bil'am, refer to Bamidbar 22:5:151:1-5.)
Why did he say "Lo Yeshaker v'Lo Yinachem"?
Alshich #1: Even though Hashem will not retract from tearing [permanent] kingship from you, He will also fulfill His word "u'Melachim me'Chalatzecha Yetzei'u" (Bereishis 35:11), i.e. two kings will descend from Binyamin, who was not born yet. Also your son Ish Boshes will be king.
Me'iri (Horiyos 11b), Alshich #2: Hashem already gave Yakov Ru'ach ha'Kodesh to say "Lo Yasur Shevet mi'Yehudah" (Bereishis 1:15; permanent kingship will only be from Yehudah). From the beginning, your kingship was 'borrowed' (Me'iri - until there will be someone in Yehudah proper for kingship 1 ; Alshich - for Amalek must fall to Binyamin. Shmuel said so to alleviate Sha'ul's worry. 2 )
Malbim: The bad that He said to do to you is not a false exaggerated threat. He will not regret the good that He said to do to David ("your colleague better than you").
David became king only two years later. Perhaps David was not proper for kingship until he was pursued so much, and twice passed up an opportunity to kill Sha'ul. (PF)
What is the meaning of "Lo Adam Hu Lehinachem"?
Radak: A person retracts from good that he promised to another if he gets angry at him, or his heart changes, and he is not as pleased with him as before. Hashem's desire does not change. Once He promised Yisrael, He will not falsify His promise for good. If they sin, He will afflict them for it, but the good will be fulfilled after they received their punishment. Sha'ul was not promised permanent kingship; had he guarded Hashem's Mitzvos, his kingship would have lasted, and also his sons', as long as they guarded His Mitzvos. David was promised eternal kingship. Even if it ceased from his sons for a while due to their sins, it will return after they receive their punishment - "when he sins, I will afflict him? My Chesed will not depart from him" (Shmuel 2 7:15).
Targum Yonasan: He is unlike people who say and falsify (do not fulfill their words), who decree and do not fulfill.
Refer to Shemos 32:14:151:1 and the note there.
Malbim: Do not think that Hashem's promise is like that of people, who sometimes lie immediately, and say exaggerated threats and their hearts do not intend so - and sometimes they truly intend, but later regret and do not do. Hashem is Eternal; there is no change in Him in the present or future.
Abarvenel: Hashem will not retract because Sha?ul is not a man who retracts from and regrets his sin; he persists in his evil.