Stitches keep popping through. Is this normal? (Photo)

Yes, this is not unusual. Particularly around the nipple. Most of these stitches are dissolvable and will take care of themselves, but I'm glad that you've been speaking with your surgeon. It's always best to err on the side of caution.

The skin around the areola is thin and as the stitches work their way out, you may feel them. These are most often  dissolvable to you can leave them alone if you want and they're not poking you. Good luck.