This completely happened to me with my last pregnancy!
I passed out many times a day for 6 months straight. They wouldn't let me drive, I couldn't stand up for 10 minutes, even sitting I passed out a few times...it was awful!
I had the not breathing feeling, then my vision would go, get really hot, then I would be out, and if I had not already laid down, I would just completely fall wherever I was. I was in the ambulance twice, overnight in the hospital, had every test done as well...etc. They never found anything out. They had no idea what to do with me either. The week the baby dropped, I never passed out again. She was sitting very high (I was measuring at least 10 cm--15 cm ahead for those 6 months) so I think that had something to do with it.
I am now pregnant again and have had probably 10 episodes of this, but nothing like my first pregnancy. As long as you stay safe (DON'T DRIVE), I don't think it harms the baby. One thing that is hard is that when it is happening you are not able to fully understand what is going on or make a decision to lay down. I used to think it wouldn't happen, of course it always did, but I did get better at laying down after a while. I did hit my head a few times though! I know it is terribly uncomfortable and rather hard to deal with. I had a note on my cell phone: EXPERIENCES PREGNANCY RELATED FAINTING-PLEASE CALL HUSBAND, and my school had to use it once because I passed out while teaching my first graders!! (I soon after had to stop teaching)