It sounds like you have multiple entries for your brokerage login stored in Safari. [I've had similar happen to me in Firefox after a site changed subtly and required a renewed login; both logins were saved, rather than one replacing the other.]
I don't know squat about Safari 9 or 10, but if they're anything like Firefox you can examine "Saved Logins", delete your brokerage login which would also delete its password — making sure that you don't have multiple entries for your brokerage login — and then re-access the site, permitting the login to be saved.
If this is the way Safari 9/10 works, then all should be good.
If it isn't, then your brokerage site is at fault, not Safari (or so 'twould seem to me).
