wow, it's amazing that a hospital-based midwife waited as long as she did! I recently had a homebirth where we waited for three hours for the placenta. As long as there is no bleeding, it's fine to wait awhile.
I would say that more than likely it's due to the pitocin induction rather than your body. When we are induced with Pitocin, it seems that our receptor sites for oxytocin are filled and natural oxytocin is hard to come by. Therefore, even with more Pitocin after the birth, our uterus may not "get the message" to continue contracting to release the placenta.
There are quite a few things I try, from nipple stim from baby, to getting up and sitting on the toilet, herbs, etc.
I don't think that your body necessarily failed at giving birth or birthing the placenta. Obviously, your body had a timetable figured out and it didn't correspond with what was set up for you.