WretchedEarl
The bank I use maintains a list of people I allow to access my box along with their physical signature. When I needed to access my box, I had to sign in with a pen, on paper and show my ID. They compared that signature with the one I gave when I first obtained the box. I was granted access if they matched. If someone else came in with the key but their name wasn't on the bank's list or the signature didn't match, they wouldn't allow access to the box.
So make sure people you want to be able to access the box are on that list (which means they will have to go to the bank to provide a signature ahead of time.)
That's not necessarily a sure cure, depending on the hosting provider. RoadRunner (Spectrum / Charter) in the US and Shaw in Canada won't deliver emails from my domain hosted at Runbox.com (or sent directly from the runbox.com domain.) Spectrum's bounce message references an error code that translates to "Spectrum limits the number of concurrent connections from a sender, as well as the total number of connections allowed. Limits vary based on the reputation of the IP address. Reduce your number of connections and try again later."