Are you using your active key to sign in to steemitwallet.com? The active key is not cached because that would put them at risk re: hacking. If you are using your posting key to sign into steemitwallet, this should not be happening. Also if you sign in with your master password this should not be happening because that is used to derive your posting key which would then be cached.

So if you're using your active key then this is the desired behavior, but if not, let me know as that would be a bug.