I notice when I make the bone broth soup, the bones get so soft, it is almost starting to disintegrate.  Could I just re-use it again for the next batch of soup I make, and continue recycling it in subsequent batches until the bones are completely disintegrated?

Also, when I strain the ghee through a coffee filter, it seems to take a very long time.  If I try to find a strainer with bigger holes, will that defeat the purpose?

I use a small cup size strainer works just fine.  Not sure about the bone question. I'll be interested in see what is said. I'm hoping to have plenty of soups this winter.

use fresh raw bones everytime....
also fish with bones and heads and tails make nice fish broth.....discard all once done

What if I were to make the next batch immediately after the first, so that the bones aren't sitting around getting old in the refrigerator?

On the ghee filtering question --

I never use filter papers.  Just get one of the very finest stainless steel strainers.  It works perfectly makes the process simple and fast.

By the way, don't stir the ghee during making.  Leave all the sediment to fall to the bottom and that way when you pour off the ghee, there isn't as much stuff to filter out.

I use a fabric strainer, as I couldn't find a steel one fine enough, and it works great. I just squeeze out the ghee left in the fabric when it's all filtered and I do stir the ghee every once in a while, but I also peel off the solids on top. That way not much on the bottom in the end

I strain my ghee through a fine mesh strainger into a pyrex bowl and let it cool a bit.  Any sediment that didn't get strained out settles on the bottom of the glass bowl.  When I slowly pour it into a mason jar, I leave that little bit of sediment behind.  Only a small amount of ghee is lost that way.

About the bones...I think once you've simmered them for a long time (I simmer my bones in a crockpot for around 24 hours or maybe more), you've already extracted all the nutrients into the liquid.  If you simmer them a second time, I can't imagine there would be much left to extract?  Give it a try, though, to see what happens.  I'd love to hear back if you do.  

Yes, you can re-use the bones. Here's a blog about a family that did just that: http://www.traditional-foods.com/bone-broth/

I don't strain my ghee through a coffee filter; I'm afraid that too much of the good stuff will stay in the paper instead of getting into my glass jar. I  bought the finest mesh strainer I could find and use that. I do get some sediment on the bottom of my  ghee container though. If your family is super-sensitive to trace amounts of milk solids, you may want to stick with the coffee filter method. I react just fine to butter, so I don't worry about a few "butter solids" in the finished ghee.

If you let the pot of ghee sit for a while to cool down a bit and then pour slowly with no stirring, you won't get as much sediment in the bottom of your ghee jar.  (I don't get any sediment)