Well, that's part of the high price...that's the channel that was deliberately cut into the outsole to hide / protect the outsole stitching. It's supposed to be glued down and only wear away slowly. But sometimes the glues being used are water based. If you got these shoes wet....so that the soles were absorbing water and the sealing glue was water soluble...this is bound to happen.
I will say it's a perennial problem for shoemakers large and small. All purpose is neoprene and toluene based, waterproof, don't require clamping, and are environmentally hazardous and probably toxic. They also leave a rubbery residue at the edges that resists waxes and other finishing techniques.
The traditional pastes are all water and starch based; are non-toxic. easily made and disposed of and finish up nicely. They do require clamping or pressure and will dissolve and loosen when wet.
Take it to a shoe repair and ask them to re-glue (and hammer) it with all purpose.