Possibly Shoe Goo, or a polyurethane, like Gorilla Glue. Both are waterproof and flexible, but need clamping during the cure, or it looks botched... If you are not DIY inclined, a good shoe repair shop could do it for a small charge, using a special contact cement. When you next replace the strap, order a waterproof leather sport band. They have waterproof adhesives, and are stitched full length for good measure. Most "dress" leather bands are cheaply made, and come apart with perspiration or occasional wetting.