So as far as I can tell, and I have asked a few Japanese people that I work with, 探す is used mainly when you know exactly what you are searching for and maybe with a little help it is in sight when you find it. 探る is mainly used when you don't really know if you will find the object or if the object is out of sight causing you to search with your hands or feet not your eyes. Two examples of 探る would be looking for a criminal, as you don't really know if they are still around or if the person is guilty, and it is used when something is behind something else so you need to blindly reach your hand into an area to search for it.
Edit: 2-24 8:17 JPT
So I asked around some more and it really looks like if there is a target for your search then you would use 探す. 探る is used when you are looking but for something but no clear target in mind or if you cannot physically see it. For the criminal example above you would use 探す once you know who the criminal is as you now have a definite target. You would continue to use 探る when you are gathering evidence before you know who they are as no clear target has been found.
