Are people ever refused abortions after having a few?

In answer to your questions:
Do they still do that?
No

If they do, how do they keep track when people give false information all the time?
They don’t.

Can a doctor know if a woman has had several abortions?
Not unless she tells him/her

She was told it would be dangerous and possibly make her sterile.
Is that true?
No, although any interuterine procedure increases the risk of sterility, no matter what it is. There’s nothing special about abortion, though in that regard.

Can the morning after pill also make women sterile if over used?
No.

Hope that helps!

Thanks for your clear answers. :)
I like it when a person is thourough.

I know that in the former Soviet Union, multiple abortions were incredibly common…my mother’s had a dozen, at least, before I was born..and I, too, would have been an abortion but the abortion doctor wasn’t available..true story.

The process used to be very different, and could cause a woman to become sterile. The process has become quite a lot safer, and there’s no longer a risk of infertility attached.