The hide will probably last as long as the meat.Personally,if I want to keep a hide,I don't try to find out how long I can let it go,but I get right on it and get it done.Technically the spoiling process begins at time of death.If I am going through the expense of tanning something,I don't want to risk getting a hide back with bare spots.Therefore I always err on the side of caution and get the hide off fresh,flesh it and get it salted.You can skin a deer in an hour or often,a lot less.Like I say,you do have some time but if you want to be absolutely safe,do it fresh.I'm sure a day won't hurt but don't push it too far.