You might also check out some of the tutorials on this demanding movement: 

In Season 2 of Step by Step, Brenda breaks down Chaturanga and Upward Facing Dog. 

Or just go "Hands-Free" with Sarah in this episode.

As you'd said "simply continuing with the practice again and again" isn't always the answer to resolve an ongoing issue. If it isn't working, and there's pain, we'll need to change something. Without having seen you chaturanga, I would caution you to modify this likely culprit. You might take a high plank with straight arms and  broad collarbones, never coming down to chaturanga. The importance of shoulder alignment can't be overstated, please refer to the Broad Collarbone Experience tutorial for more details.....

Another great place to revise position, is within the hands themselves. The fingers should be really spread far apart. I used to suffer from wrist pain until I learnt to spread the hands so much that my thumbs are almost exactly parallel, pointing directly towards one another. This helps to ground the index finger mound, the knuckle where the finger meets the palm. Do make sure this is staying grounded whenever your hands are on the mat. We keep weight away from the wrists, especially the pinky side of the hand. Instead, direct pressure towards the front and index side of the palm. I hope this is helpful. Please do keep me posted and be in touch with any further questions ! Let's get you comfortably on the mat! D