According to Baptist theology why doesn't Satan surrender?

Hebrews 2:16 says, “For surely it is not angels that he helps, but he helps the offspring of Abraham.”

Jesus is THE savior, and he died to save mankind, not angels.

See http://www.reclaimingthemind.org/blog/2012/09/can-satan-be-saved/

Since Satan's final punishment and imprisonment is made clear in Revelation 20 and elsewhere, he has no expectation of forgiveness and pardon. If the times are set, he can neither lengthen nor shorten his time of freedom.

10 The devil, who deceived them, was cast into the lake of fire and brimstone where the beast and the false prophet are. And they will be tormented day and night forever and ever.

First, "Baptist theology" is too general a term for a specific question which itself is a rather peripheral issue that is unlikely to see a uniform answer even from within one denomination. Therefore I do not think it can be answered except as regards general principals of theology.

Baptist typically hold to either Arminian or Calvinistic theology. If dealing with the latter, the answer would be that the devil was foreordained to damnation, thus he cannot repent/surrender, and does not want to. The Baptist Confession of 1689, subscribed to by English Baptist Ministers in the year 1689, states that "By the decree of God...some men and Angels are predestinated, or fore-ordained to..being left to act in their sin to their just condemnation..."

Contemporary Baptist theologian Wayne Grudem states that,

Such are held to be reprobate: "Reprobation refers to God’s eternal decree to refrain from providing saving grace to particular fallen individuals and to harden these in their willful sins..." (https://www.monergism.com/election-and-reprobation)

Arminians believe that the devil and his angels had the freedom and ability to obey God, but chose to disobey, and they believe, as the Arminian Confession of 1621" teaches, that those who "are guilty of prolonged defiance and rebellion" are liable to God "blinding, hardening, or delivering them to the efficacy of error, to their own corrupt desires and to a reprobate mind," and that the devil will be cast into everlasting fire. (http://evangelicalarminians.org/the-arminian-confession-of-1621)

The Bible warns about becoming "reprobate," a condition resulting from rejecting the light and grace one had, and hardening one's heart against it. Heb. 6:5-9 speaks most clearly about such:

And have tasted the good word of God, and the powers of the world to come, If they shall fall away, to renew them again unto repentance; seeing they crucify to themselves the Son of God afresh, and put him to an open shame. For the earth which drinketh in the rain that cometh oft upon it, and bringeth forth herbs meet for them by whom it is dressed, receiveth blessing from God: But that which beareth thorns and briers is rejected, and is nigh unto cursing; whose end is to be burned. (Hebrews 6:5-8 KJV)

Also (2 Corinthians 13:5 KJV)

Examine yourselves, whether ye be in the faith; prove your own selves. Know ye not your own selves, how that Jesus Christ is in you, except ye be reprobates?

(Titus 1:16 KJV)

They profess that they know God; but in works they deny him, being abominable, and disobedient, and unto every good work reprobate.

In contrast (Hebrews 6:9 KJV)

But, beloved, we are persuaded better things of you, and things that accompany salvation, though we thus speak.

The devil is surely one who has "tasted the good word of God, and the powers of the world to come," having know a level of light and blessing unknown to us, but who selfishly exalted himself as one worthy to sit as God, whose power and glory he lusted after. (Isaiah 14) This was the first "Occupy Movement" if you will, climbing up some other way to honor than by grace and the merit of obedience.

Thus, being cast down due to his unholy presumption, he worked to seduce Eve with the victim-entitlement message, that she was entitled to the one thing forbidden her amid myriad blessings, which one thing (as the devil construed it) God was selfishly keeping from her least she be as God - rather than "sharing the wealth" - and thus she should just take what she wanted, and that instead of the (unjust) punishment for such presumption, she would be as God.

But like souls in Hell, she found out the hard way that the devil deceived her, to her own hurt, while the devil gloried in his gain. Which he yet seeks via proxy servants in false religion and politics.

(John 10:10 KJV)

Verily, verily, I say unto you, He that entereth not by the door into the sheepfold, but climbeth up some other way, the same is a thief and a robber.

(John 10:1 KJV)

The thief cometh not, but for to steal, and to kill, and to destroy: I am come that they might have life, and that they might have it more abundantly.