I have a daughter in gymnastics and I am taking action pictures from fairly far away with bad indoor gym lighting from sometimes quite a distance.

Try some of these settings, recommended by one of our camera experts, James Deruvo, many have found them very helpful:
1. Prefocus. Hold down the shutter half way to get a prefocus of the image you're shooting. When it changes, prefocus again. This will speed up your camera's performance during picture taking since it won't have to autofocus before it shoots the shot.

2. Use faster SD cards. Yes, there are faster cards and it does make a difference in writing the image file to the card. This is especially key if you're taking multiple or burst images.

3. Fresher batteries. Use alkalines at least. But I recommend using high energy batteries designed for digital photography. Varta is a good brand. They are usually sold in camera shops, are long lasting (because they are sold in small quantities) put out alot of energy.

4. Pan with the action. You can create some pretty cool shots by panning with your shot, focusing on your subject. This will create the effect of your subject in sharp contrast to the blurry background.

6. Stick with 100-400 ISO. Going higher will cause more noise/grain in your shots, particularly in darker settings.