This is very common with expensive hiking boots, which use a soft, but less stable type of rubber. The process is called hydrolysis and is due to the ageing of this soft rubber. The rubber loses strength itself and becomes crumbly; it is not a glue issue.
In my experience, glue does not work.
I had a very high quality boot with the Vibram soles in near pristine condition. Soles fell off. Took the shoes to a cobbler, who glued on the soles using rubber cement.
The shoes looked like new, but completely fell apart on my next trip.
I took them back to the cobbler, who specifically ordered the glue recommended by the manufacturer of the shoes. (It was either a neoprene or polyurethane glue, I don't remember).
Again, the repair looked perfect, and again the shoes fell apart on a trip.
This is very dangerous, because the process starts in the middle of the shoe, until the sole is only held at the edges. Suddenly, the whole sole will come off in one piece.
I fixed the shoe with Gorilla glue, which worked long enough to get back home.
The manufacturer claimed that they could replace all of the aged rubber (cost ~$100), it looks good, but I haven't tried it yet. They did not simply glue on a new sole, but they ripped off all of the rubber parts down to the leather and replaced those.
Things that I learned:
- Glues do not work, even when done professionally. In my case, the sole looked like new. There was no glue residue left on the underside of the shoe. The surface of the shoe looked perfectly clean, and I thought it would be simple to just glue the sole back on.
- This is a major safety issue. Imagine your shoes suddenly falling apart in the middle of nowhere. In the best case, it will be a long drive to buy a new pair of shoes, ruining the vacation.
- Of all emergency glues, Gorilla glue worked best.
- Gluing the sole on on the trail is not easy. It needs a lot of pressure to keep the sole in contact with the rest of the shoe. The glue needs to harden for at least a day.
- It is a good idea to have an awl and some dental floss to sew the sole to the shoe before gluing. Especially the rounded needles came in very handy. (search on ebay for "canvas repair stitcher").