Kathleen Auerbach sent the following to me (thanks very much Kathleen).
Thought I'd share it with you all.

The major dictionaries FOLLOW rather than DICTATE usage.  Some years ago, I
did a search of the medical literature and discovered the interesting
pattern.

a) first used was the two word form:                breast feed
b) followed in later years by the hyphenated form:  breast-feed
c) with increasing compound single word use today:  breastfeed

At JHL, we made a deliberate decision to go with the single compound form.
Our goal is in distinguishing breastfeeding from mechanical forms of
feeding, such as cup feeding or bottle-feeding, etc.

The more people who use the single compound word form, the greater the
likelihood that it will be viewed by all as the PREFERRED form and that the
dictionaries (Oxford, etc) will show it as the preferred form.  Hope this
helps.