Hershell and Willofig, you never know :-)
Jon and Joe, thanks!
Harvey and Andreas, I find that girdling is not necessary for my application because the whole set-up isn't very heavy and also because the air layers aren't usually on the tree very long. It only takes 3 weeks in Summer for air layers to root in my climate. I simply use a cotton string at the bottom and top openings of the bag which I tie tightly. I like cotton for its better friction which prevents loosening of strings over time. This helps prevent rain water from getting in as well as drying out of the soil media.
As long as my media is just right, I won't usually find any decay. I've had several branches flop over after a windy spell and with a little investigation, that is when I realized that low-friction strings loosen over time which then allow rain water to get in. A couple of weeks of "wet" soil rots the branch enough and a little wind will expose the weak link.
I like to use those air-filled plastic cushions that are used in shipping merchandise. I simply open both ends, slide it over a branch, tie the bottom, fill with media, tie the top, and cover with foil. For bigger branches, I've had to order 4x4x9 bags (I could be an inch off somewhere but you get the idea).
I hope I explained it clearly.