Don't know of anything really automated, Winslow Automation offers solder spheres on water soluble tape and a company called the Waveroom Plus in NH offers a machine reasonably priced but it is not automated. There are companies out there that offer reballing services however.
We might need to open up the term "mass production" here, but I will give it a try anyway.
I've seen semiconductor packaging companies in the far east where they pick up balls with a vacuum head, consisting of holes matching the pattern of the BGA pads lying underneath with flux. Then these balls are lowered and the parts go through the oven.
The methods I offer to my customers are:
1. Winslow BGA profiles 2. A mask + loose balls
The second method is good for relatively higher volumes.
I also recommend the flux-pens to apply flux on the pads prior to placement. Some people use gel flux instead.
The Winslow method is good for lower volumes, while the profiles are sold in multiples of 25. Depending on the value of the BGAs you need to reball/save, Winslow method is an easy one to implement. I have customers using the Winslow profiles for BGAs valued at around US$100, up to US$300. Very good savings, that's for sure.
I don't wanna say one method/brand is better than the other. Second method requires more work, costs less.