It would be quite simple to perform pulse oxymetry during a feeding  to
determine the  degree of oxygen desaturation  while breastfeeding.  In
babies, the oxymeter probe is often taped to the toe, and this baby is
probably monitored continuously or frequently anyway.
Monitoring throughout a breastfeed  would enable to doctor, as well as
the mother, to really see what is going on before deciding that the
mother should not breastfeed.

I would suggest this, as well as the reference from Journal of
Pediatrics.

Yael Wyshogrod
Rehovot, Israel