This is an interesting question. I used to skin and process game animals in our family's little custom meat cutting establishment. The problem with trying to count the number of deer skinned without sharpening is people perform different tasks when they skin. If you are just talking skinning, without field dressing, removing the head, removing the legs at the knee joints, you should get quite a few deer before requiring sharpening--even with a "not-so-sharp" knife. Properly done, there is little knife work in skinning deer. The knife starts the process and is used a little around the legs and head, but most of the hide is pulled or "fisted" off the carcass. Now is you have to cut the legs at the joints and sever the head at the "atlas" joint, you need more knife action--knife against bone--which dulls more quickly. Also, lots of hunters refuse to buy a small pocket saw and use their knives to split the pelvis and rib cage. The majority of broken knives happen when attempting these two activities. If you know where to split the rib cage--just either side of the sternum in the cartliginous material that attaches each rib to the sternum--you can run your "fixed blade" knife up the line and split it. Sometimes a folder will work, but this is where many hunters break their knives. Either buy a saw, or leave it for your processor to do.
I carry a 4" blade, custom semi-skinner hunting knife and a small Gerber folding pocket saw. I can process about 10 deer before I need to even think about sharpening.
Bruce Woodbury