placenta giving out...

Xanthia
With my first baby (she's 4 1/2 now) my placenta "died" around 6 months into my pregnancy. They didn't catch it until I was 38 weeks and I was induced the night they found out because there was little to no fluid and she was dying as the doctor put it. After I had her the doctor told me I wouldn't have to worry about it happening with any of my future pregnancies because it was so rare and hardly reoccurs. 
I am 12 weeks today with my second baby, and I also have a different doctor this time. Today at my appointment I asked the doctor (for good measure) if I needed to worry about my placenta giving out with this baby. He said there's not much to worry about, but they are going to have to keep an extra eye on the baby's growth and amniotic fluid levels because there's a good chance it could happen again. 
So I guess my questions is if anyone has had their placenta give out, and if so, did it happen with more than one of your pregnancies?