Does this database consist of multiple files?
Since each file has its own set of account names and privileges, changing the password for one file could trigger a "cascade" of password change dialogs as each related file attempts to open. You normally don't get these, because when a relationship or script triggers the opening of a related file, it attempts to open the related file with the same account name and password as was used to open the current file. It will only ask for a password when the account name and password that opened the current file is not found in the new file.
That sounds like what you've encountered.