I was told early on that I would have to come twice a week from week 32 on. It just so happened that I've been going twice a week since week #30 because we had a couple of non-responsive non-stress tests - so my dr. had me come back to make sure everything was OK (and it was thank goodness). When and if you happen to get a non-responsive non-stress test, they will send you for a biophysical profile ultrasound where they measure several things. Movement, breathing, amniotic fluid etc. It's out of a score of 8 (it's really out of 10, but 2 points come from the NST, so if you don't pass that it's out of 8...which is why you' be sent for the biophysical profile ultrasound in the first place...anyway) When we got the two non-responsive non-stress tests my dr. said if I didn't get 8/8 to come back and see him (not sure what would have happened if we didn't get 8/8...he mentioned coming back later in the day to check again...or possibly sending me to the hospital for them to monitor), but thankfully we passed with 8/8 both times so far.
I think you and I are about a little over a week or so apart right now. I'm about to start week #33 on Friday....which is when my next NST is as well as an ultrasound so they can do measurements. I am exicted to find out how much the baby weighs now...she was 3 lbs. 8 oz back on 3/17, so hopefully our little angel has packed on some weight! :o) The Dr. used a measuring tape yesterday to measure my belly and said I was right on target. My most recent Hemoglobin A1c was 5.4 and I am in the best control of my life. He said I was doing a good job and it made me feel really good. How have your numbers been?
I asked yesterday at my appointment what was next as far as the testing goes and the dr. told me that week 35 they will do the strep B test...which from what I have heard is similar to a pap test.
As far as the non-stress tests becoming more frequent after 36 weeks...I haven't heard that from my dr., but I suspect if there were several non-responsive ones, they would probably send you for monitoring more frequently. Are you going to be induced? I was told from the beginning that I will be induced and we just talked about dates for the "main event" yesterday. I'll go for an amniocentsis on 5/14 and then if everything is OK with that (they check for lung maturity before induction) they will induce on 5/17.
Good luck with your tests! Let me know how it goes!