How do I get the eye dropper tool in Lightroom 4 Develop module to stay on? When I move the eye dropper tool across the image it turns off, and then sometimes turns back on again. Can anyone tell me how to keep the eye dropper tool on, or is this a design characteristic I do not understand?
This is not normal. Are you sure you're using it correctly - ie, rather than just dragging it off the sidebar, you click it once and then the circle it was in becomes empty, and your mouse cursor changes to the dropper. Then you move it over the image and use as you wish (eg to select neutral grey for white balance etc). When you are finished take your cursor back to the circle from whence it came and click again to drop it back into there.
This isn't a typical situation. Are your sure your mouse or pointing device is powered correctly? If so, I would start by resetting your settings. This has information on completing that: http://help.adobe.com/en_US/lightroom/using/WS82DA0B67-FA83-4c71-84B9-6F248A97FBE8.html
If that fails, you could reinstall Lightroom. If that doesn't resolve the issue you might have found a bug and you should contact Adobe.