The question is bit confusing;
His car is in 3/4th gear at 5~10kms, problem car does not respond when he accelerates in these gears. (How will it)
Then he says that he either has to downshift or accelerate. (This is normal So where is the problem)
You should first down shift then try to pick speed. Have you tried this and face same problem?
@umar47.....is my interpretation correct?