In our daughters case they think it is reactive, we go this morning for another set of test and hopefully the count has continued to come down.
She had an ear infection that we thought had cleared up after 10 days of medication, then she got a cold, and then as she was getting over the cold she had another ear infection, likely the same ear infection as before. This is when we noticed the high counts after her being sick for about 5 weeks with various things. Her other blood counts were all normal, it was just the platelets that were high.
Our pediatric hemo doesn't seem to be to worried as long as the counts are below a million, and I have seen many stories of people who have slightly higher counts without any associated medical problems. If you babies counts continue to go up I would look for some type of infection that might be hanging around.
I understand your frustration, there really isn't much good information out there on this for infants. If my wife or I find out any information we will be sure to pass it along, and please do the same.