Is there a reenforced tape or similar that can be applied to a new App

I bought a brand new, factory sealed Apple Battery Case for my aging iPhone 7 as a way of getting longer daily use without the need to recharge during the day. Was very happy with it for 4 1/2 months or so when the case started losing small flecks of the rubbery edging of the case. Then about a month ago, a piece of the edge came loose, eventually breaking off completely on the right hand top corner, and then a smaller piece broke off on the upper left hand corner. I seriously doubt Apple will do much of anything for me with my case, but I really enjoy the ability to go all day without having to recharge the battery as much. I'm thinking about buying another Apple battery case and would like to protect it from suffering the same fate, so I was wondering if anyone has an idea about reenforcing the top outer edge of the case with some really strong, really thin tape product, possibly something reenforced. Would appreciate any suggestions.

This is a picture of the case after one corner of the case broke off, since then the other top corner also broke off. This is for an iPhone 7, I really like having the extra battery capacity and will buy another new Apple battery case if I can protect it so this doesn't happen again, that's why I'm wondering if there is some sort of very thin, very strong tape or band that could be applied to the edge of the case to prevent a new case from breaking down. The case pictured is six months old, was purchased brand new in factory box.