I had to do kick counts towards the end of my pregnancy because ultrasounds showed that the cord was around the baby's neck and she was already head down and engaged. SO they were concerned about the cord and scared me half to death. When she was born... the cord was NOT around her neck. I am still a little annoyed about that because I was terrified towards the end.
Leading up to labor... I didn't notice a decrease in her movements. I was induced 5 days before my due date so I don't think she was quite ready to come out.
She still moved quite a bit while I was in labor. I had the external monitors on my belly and you'd see my belly move since she was pushing at the monitors