"Everything I have read says 2-3 CBC's should be done per week for 6-8 weeks."
Hi, for starters, I'd think that what you need is an 'authoritative' source. My guess is that this one qualifies, since it is from ASH: It also gives the reason, which seems logically very valid. (I don't see a date on it, though.)
"It is imperative to establish the diagnosis of cyclic neutropenia by serial differential white counts at least 3 times per week for a minimum of 6 weeks to observe at least 2 neutrophil nadirs."
http://asheducationbook.hematologylibrary.org/content/2012/1/174.full
So you might ask the hema why they are doing differently. It might be because your child hasn't been proven to have the gene mutation at his point.
However, if it looks that the hema seems not-too concerned, maybe that is because of something like this from Medscape:
Pediatric Autoimmune and Chronic Benign Neutropenia Differential Diagnoses
https://emedicine.medscape.com/article/954781-differential
"Acute transient leukopenia and neutropenia in small infants and young children are extremely common."
and
"AIN of infancy usually lasts at most 2-3 years before spontaneous resolution. If it persists beyond age 4-5 years with a benign course..."
But all that with children is outside of my sphere, so I really don't know. Children generally have exaggerated immune reactions because their immune systems are still forming.
Btw, I also don't see very low abs neuts. Again, from ASH:
"The risk for infection in the disorders of neutrophil production and release is greatly increased, with counts of 500-200/μL, and is very severe below 200/μL. "That might make you feel a little better.
I'd also ask if the rashes should be expected in neutropenia. If not, remember that as a possibly important clue if the neutropenia diagnosis doesn't apply. That's especially so if there is a family history of odd immune conditions separate from neutropenia.
"His neutrophils are normal while sick, normal lymphocytes too..."
When you get the flu, all your symptoms are from immune system chemicals, not directly from the invading pathogen. It's possible that his bouts of seeming infections are also only immune system reactions.
Monocytes can orchestrate immune reactions. Like a general telling troops what to do.