To bad Fords are cheap-skates with no inner bearing race. Buy another axle from Ford and replace the seal.
What ever the reason, its not sealing. Probably a burr or groove on sealing area. If you have a replacement, I'd go for it.
Yes, the axle should have been changed, because any axle movement will cause premature wear on the seal. Try the used axle, and change the seal again. Leaking oil is not acceptable, since you won't be able to track the level easily. Not to mention the brakes and softening of the tire rubber.
also something no one has touched on, the vent may be plugged, and thatll do it. the new side will leak faster than the older, could be bad bearing, workmanship, parts, etc.
if seal was not install correctly or where axel seal rides on shaft is worn or ruff ,will do that they sell a repair sleeve to slide on axial or emery paper axial
i had my rear axle shaft seal replaced and my wheel bearing in my 1997 town car a week later/1000 miles it started back leaking, what would cause this, the axle did have a little grove in it due to a bad wheel bearing, so i asked the mechanic he said its not bad enough to cause a problem so he gave me something called a fix it bearing which would off set the axle ride a little bit, could it be the axle shaft itself causing the leak, i have a junk car with identical axles, i'm thinking about just replacing the axle, i just topped off the diff, my brakes aren't wet just the inner tire is wet, what do you think