I for one am not the kind of parent who sits by when a doctor tells me that after repeated visits that my child will be OK. Not that your docs are bad docs, they just don't have all of the answers. I'm also not saying that something is terribly wrong with your child. I'm not a medical doctor, but have experienced recurring sickness in my child only to find out a year or so later that something WAS wrong and "why did you alert us?" ARGHHH!!
I found this article for you to look at:
Recurrent Fevers in Children: Differential Diagnosis - February 15, 2003 - American Family Physician
What type of blood tests have they performed? the end of the above article states that there are instances where a child simply has fevers and grow out of them..but as a parent, I totally understand your need to get an answer.
Be sure to keep good notes and all test results just in case you do need them for future visits. You may aslo want to try to see another doctor for a second opinion. Sometimes having 'fresh eyes' look at your child's folder brings something out that the first doctor didn't see. AGain, not because the first doc is bad, just overwhelmed with his/her case load and the file is becoming "familiar' in that he/she may be missing something.