There is a boot and two clamps that hold it on. On some of those clamps, one ( can't remember which ) isn't made right and it won't tighten up properly. It's possible to fix that problem by looking at how it's made and making adjustments to the overall length.
Aside from a loose clamp or a crack in the boot, the only other thing you might find is a broken diff housing caused by not having the axle tube supported when changing the right side shock. The axle tube can drop with enough force that it will knock a chunk of cast iron out of the bottom of the housing. Since the boot and clamp covers this area it's easy to assume that the boot is leaking. Maybe not what you want to hear but you should look for this.
The cure is as bad as the problem. Axle would have to be removed and taken apart. It is possible to have it welded but it's a lot of work to get there. Hopefully, only the clamp or boot is faulty.
