Hi bobw61852213 ,
Would like to inform you that we cannot set the password to be remember with the pdf files.If document is secure, on every opening need to enter the password.
Also refer to this article :-https://helpx.adobe.com/acrobat/using/securing-pdfs-passwords.html
If you can open a password-secured PDF without providing the password then everyone else can as well which negates the security. Acrobat provides two forms of authentication: password and certificate. If the producer of your PDFs uses certificate encryption then anyone who has a proper certificate installed on a specific machine can open certificate-secured PDF on that machine without having to enter password. There are also server-based solutions to secure PDF which allow a user who belongs to a certain group to open PDFs secured for that group without entering passwords These solutions are not simple, though.