Earlier, Judges 2:14 uses the same language:
So the anger of the Lord was kindled against Israel, and he z gave them over to plunderers, who plundered them. a And he sold them into the hand of their surrounding enemies, b so that they could no longer withstand their enemies.
If they exchanged the worship of the LORD for other gods, then it was a national transaction of sorts.
God was just handing them over to the masters they served.
Notice in the Judges 10 passage that the "repentance" seems superficial and the Israelites were choosing whom they served:
6 l The people of Israel again did what was evil in the sight of the Lord m and served the Baals and the Ashtaroth, the gods of Syria, n the gods of Sidon, the gods of Moab, the gods of the Ammonites, and the gods of the Philistines. And they o forsook the Lord and did not serve him. 7 So the anger of the Lord was kindled against Israel, and p he sold them into the hand of the Philistines and into the hand of the Ammonites, 8 and they crushed and oppressed the people of Israel that year. For eighteen years they oppressed all the people of Israel who were beyond the Jordan in the land of the Amorites, which is in Gilead. 9 And the Ammonites crossed the Jordan to fight also against Judah and against Benjamin and against the house of Ephraim, so that Israel was severely distressed.
10 And the people of Israel q cried out to the Lord, saying, “We have sinned against you, because r we have forsaken our God and have served the Baals.” 11 And the Lord said to the people of Israel, “Did I not save you s from the Egyptians and t from the Amorites, u from the Ammonites and v from the Philistines? 12 The Sidonians also, and w the Amalekites and the Maonites oppressed you, and you cried out to me, and I x saved you out of their hand. 13 Yet you have y forsaken me and served other gods; therefore I will save you no more. 14 Go and cry out z to the gods whom you have chosen; let them save you in the time of your distress.” 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.” 16 So they put away the foreign gods from among them and served the Lord, and a he became impatient over the misery of Israel.
They were abusing the Lord as a backup plan. They had already sold themselves down the river, so to speak.
God was only obliging them in their apostasy.
As I said in an earlier post, apostasy and the tendency towards it in the human heart, is a big theme in Judges. God is merciful and longsuffering and slow to anger, says Scripture... He tried to give Israel many breaks and continues to do so later on, but He isn't going to force Himself upon anyone either.
This is another interesting question. I am in the middle of finals, so I wish i had time to make more thoughtful posts, because these are the kind of passages I wrestled with for years. I really like engaging these question and I think the are entirely legitimate for us to ask -- if we aren't asking them, I kind of wonder why we wouldn't. They are awesome challenges that I find have led me to even greater appreciation, faith and love for the Lord
Peace