Natural ability? No. The best teacher money can buy? No. More hours of practice? No (Although we should only practice on the days we eat!) The secret I have observed is to LISTEN to the Suzuki recording every day for at least an hour. Of course, you do have to practice, have an educated teacher, and follow the teacher's instructions. But some of my students do practice and still struggle. I've noticed that the ones who don't struggle as much are faithful each day to do their listening.
In fact, during Suzuki Book I, I am not going to teach the pieces to the student and they are not going to read the music (we will start reading pieces in Book 2). The student is going to listen to the recording and be able to sing the piece before we begin it. Then I will teach the student how to "treasure hunt" for the notes on the violin, essentially learning to play the piece totally by ear. This is an amazing skill to have! I have met many phenomenal classical musicians who cannot play by ear. Playing by ear allows you to play all kinds of music in different situations such as rock bands, bluegrass, church worship team, fiddling, etc. We will learn to read music starting in the last half of Book I after the ear is developed. I believe it is essential to being a well rounded musician to have both skills: playing by ear and reading music.
Another wonderful secret to success is to listen to the piece you are working on plus the two following it multiple times a day. Yes, maybe 10 times in a row or for however long you can stand it! And when you cannot simply listen to your Suzuki Book any more, get the next book or the one after and start listening to it. You will be inspired to keep practicing, and your brain will already start learning the pieces in Book 4 or Book 5 or beyond. And of course, listen to all kinds of other music that use the violin or any other instrument you love. We can only play what we have put into our mind and into our fingers.
Now, go find a recording and get started!