Judges 1:19
19 And the Lord was with Judah; and he drave out the inhabitants of the mountain; but could not drive out the inhabitants of the valley, because they had chariots of iron.
Critics of the Bible present this verse as stating that God was, despite His best efforts, unable to help the Israelites conquer the Canaanites in the valley due to their iron chariots.
First, take note that the pronoun "he" in the verse refers to Judah, not God - which makes sense, because Judah is the antecedent. The tribes are frequently referred to as a single unit like this in Scripture (Deuteronomy 33:6-24, Judges 1:33, etc., etc.). Obviously, the Canaanites depended on God for every beat of their heart, just as every human being to ever live does.
Verse 19's declaration of Judah's victory on the mountain almost completes the chapter's description of the Israelite's conquests in Canaan. We only hear of one other victory 3 verses later when Bethel is conquered.
So too, Judah's defeat in the valley is the first we hear of a long line of Israel's failures to drive out the Canaanites. For example, we learn that:
Therefore we see that the Israelites had begun a practice described in verse 28:
Judges 1:28
28 And it came to pass, when Israel was strong, that they put the Canaanites to tribute, and did not utterly drive them out.
And this practice is precisely why they began to lose, as God withdrew His support for them:
Judges 2:1-3
1 And an angel of the Lord came up from Gilgal to Bochim, and said, I made you to go up out of Egypt, and have brought you unto the land which I sware unto your fathers; and I said, I will never break my covenant with you.
2 And ye shall make no league with the inhabitants of this land; ye shall throw down their altars: but ye have not obeyed my voice: why have ye done this?
3 Wherefore I also said, I will not drive them out from before you; but they shall be as thorns in your sides, and their gods shall be a snare unto you.
Therefore from verse 19, we learn that the time between Judah's battles in the mountain to when they began to battle in the valley marked a turning point where God withdrew His support. God only would give them the land if they were obedient to His commands.
This has nothing to do with God's inability, and everything to do with God withdrawing His support from the Israelites because of their disobedience.