Ah, this thread reminded me of my husband's godparents. They wanted a child for years and could never conceive. I don't know what medical procedures they underwent, but I believe they were told conception was quite unlikely. Eventually, they gave up and got on with their lives.
And then, when the woman was in her early 40s, after nearly twenty years of conception-free marriage, she went to the doctor complaining of various symptoms including persistent nausea and exhaustion, and was surprised and thrilled to find out she was pregnant.
Their son graduated from university a couple years ago, and I believe he's married now (or at least, he was engaged last time I heard).