I'm late responding to this post but I have a 'it happened to me' story to share. My husband and I met in our mid-30s and started trying for a family around our 1st anniversary. I did get pregnant but that resulted in a miscarriage which was followed by 3 years of fertility treatments (including 3 IVFs) which resulted in our beautiful boy/girl twins. Our story is included in the book 'Pregnant with Hope' that's available through amazon.com.
I was 40 when the twins arrived and after so many doctors over so many years had told us we'd never have kids and how much work it had been to have the twins I never really took the need for birth control seriously following that pregnancy. However, we did get pregnant - the 'old fashioned way' - last fall. Baby #3 - a girl, and fortuantely only 1 baby - is scheduled to arrive on July 1st! It was a huge adjustment to absorb the news of this pregnancy - it just didn't feel real or possible - we didn't share the news with our families until December because that's how long it took us to come to grips with it first.
I shared the news with my reproductive endocrinologist (#2 doctor at Cornell CRMI at NY Presbyterian - one of the doctors who developed IVF procedures). I not only shared the news of the surprise pregnancy but asked if anyone is doing research on 'fertility after infertility'. He was genuinely happy for us (great guy) and reported that there is no research that he is aware of - he reported these pregnancies are pretty common and attributed it to 'physiological changes'.
As we've shared the news of this pregnancy it's amazing how many others have had the same experience. I'm sorry there isn't more research in this area - I can't tell you how much it would have changed my outlook during those 3 years of dealing with not being able to get pregnant to know that one day it actually might happen spontaneously!
We thought we were done with 2 wonderful kids - now we're ready to welcome baby #3. This size family may not have been the 'grand plan' but it will be wonderful.