http://www.fsis.usda.gov/Fact_Sheets/Focus_On_Freezing/index.asp

It states:

Refreezing

Once food is thawed in the refrigerator, it is safe to refreeze it without cooking, although there may be a loss of quality due to the moisture lost through defrosting. After cooking raw foods which were previously frozen, it is safe to freeze the cooked foods. If previously cooked foods are thawed in the refrigerator, you may refreeze the unused portion.

If you purchase previously frozen meat, poultry or fish at a retail store, you can refreeze if it has been handled properly.”

I have also found many books and a few websites that state the same thing. And for me that was confirmation enough to go ahead and continue. But of course if you don’t feel comfortable with doing it, don’t!  Trust your instincts. Also speak with your pediatrician.  He/She may have valuable info to pass on. And of course if you find out anything from a reliable source please pass it on to us!