This happens to me sometimes if I'm waiting.
One day I arrived at Whiterun during the night so I went to sleep until close to 8. Then I went to Belathor's but it wasn't open yet, so I waited one hour. Still not open... I thought, that's weird, maybe he opens at 9 and I never realized. Waited one more hour and still not open. One more hour and nothing. Two hours and nothing. Two more hours and still closed. When it was close to 8 pm I just assumed there was some glitch from me, starring at his door waiting, so I just went to some other vendor instead.
This happens in Whiterun to me all the time. If you wait in front of the door it will never open, it's a glitch that stays locked. If you wait til 8 or 9 around the corner, then look at the door, you should be fine. Also, I've waited and the door was locked, turned away to talk to the guard that's always standing there, looked back, and the door was open.
Still funny though