What Takes The Body Longer Periods To Fight Off Infection?

I have a 4yr old who has a sister has leukemia and he is also showing similar signs that she had before she was diagnosed. I have done 3 blood test which results came back with low blood and no leukemia and also for the 3 test the doctor has told me that his body seems to be fighting off an infection. I wanna know why his body is still fighting an infection after treatment was given each time I did the blood test