'Jdg 10:13 Yet you have forsaken me and served other gods; therefore I will save you no more. Jdg 10:14 Go and cry out to the gods whom you have chosen; let them save you in the time of your distress.” Jdg 10:15 And the people of Israel said to the LORD, “We have sinned; do to us whatever seems good to you. Only please deliver us this day.” Jdg 10:16 So they put away the foreign gods from among them and served the LORD, and he became impatient over the misery of Israel.
Judges 10:16 is possibly better translated by the NJKV:
Jdg 10:16 So they put away the foreign gods from among them and served the LORD. And His soul could no longer endure the misery of Israel.
In Judges 10, God becomes so frustrated with Israel that He proclaims that He “will save you no more”. But the people repent in verse 15. They show humility and accept punishment, only asking that God once again save them. In verse 16, the people forsake false gods, and then the text reads that God’s “soul could no longer endure the misery of Israel.” God changes His mind. Although He had proclaimed against Israel to no longer save them, God reverses that position when He witnesses their repentance.
It is important to note that Israel has before been given leniency due to their suffering. In verse 14, God is repenting of continually showing leniency due to suffering. But God reverses His declaration after direct observation of their suffering, yet again. The idea being communicated is both God’s overwhelming frustration with Israel’s cycle of sin, their short-lived repentance, and God’s wasted efforts in salvation. This is coupled with God’s emotional attachment to His people, while seeing them suffer. This passage is about God’s conflicting internal emotions, and God’s commitment to Israel instead of His own declarations.
None of this would make sense in a world where God is impassible, or outside of time, or has a single “perfect” will. This is just one of many examples in which God revokes His declared intentions. In this instance, the text represents God as knowing the people would beg to be saved and would repent. God’s own repentance is not based on intellectual knowledge, but new emotional experiences that sway God against His prior judgement. God’s change is not based on calculated logic, but on passions that the people evoke within God.’
source: Christopher Fisher, “Judges 10:13-16 Commentary” (godisopen).