Just want to add to this,
It is normal for Iron Levels to drop before the birth, our blood thins a bit, (so it can rush around our bodies and get to the baby etc) Michel Odent talks about this alot, and that its a misunderstanding between the medical profession and normal birth physiology.
Obviously, some levels of low iron are more of a concern than others, but he says most of his calls are from women that have been told nearer their due date, that they are not allowed a home birth because of low iron levels, when really, their levels are perfect for what their bodies are meant to be doing at that particular stage of pregnancy.
Happened to me too, and its very common.