Try contact cement. It's not easy to work with but once together, few things come apart.
Also Loctite makes a number of excellent adhesives. I used their Power Grab, a construction adhesive for a problem similar to yours with my 3G soles. Power Grab seems to stay flexible and has stayed in place. I also use Loctite's Vinyl, Fabric and Plastic adhesive on several things and it also works well.
I find Loctite products in the glue section of Home Depot and Lowe's