ORIGINAL: it flies it dies
I didn't think that the problem was the distance they are from the camera because you can easily make out the doe in the background in the first picture and it is a lotfarther away than the doe in second and you can barely see her...
No, it is not a lot further. It may appear to be , but it isn't. And looking at your pics, yes, the first one is a little bit clearer, but that is with a fresh battery, and no sticks in the way.
The small amount of sticks in the middle and edge of the pics, can reflect the light from the flash, and cause the flash to reflect back to the camera which weakens it. Note: there are no sticks or anything in the first pic. I have been using the game cameras for a few years, and these types of things are what I had to learn by trial and error. It also matters where the forward deer trips the trigger mechanism. How close it is to the camera, and if it is centered or off to one side.