Renown catchup slows down as get closer to the cap. It took me ~10 dungeons (a combination of normal, heroic and m+) on my shammy to get from 28 to 29. Then I ran a single key, not even a high one (a +9), and went from 29 to 30. Two more dungeons, and I hit 31.
It’s a bit random, which can be frustrating. But it doesn’t stop until you reach 40. Past experience suggests that a weekly reset usually speeds up renown catchup for a little while again.