I have just built a database system in Microsoft Access and am now
trying to set the logon permissions for the database. However, I am
running into the following problem: I assigned three usernames to my system along with 3 passwords. Unfortunately, if I copy my database over to another computer off of the network drive, the database instantly "forgets" all of the logon permission information. On the contrary, if I open up an old Access database on my workstation for which I never set any logon permission, it prompts me for a login name and password and accepts the accounts for my new system.
When installed, Access has a generic user that has full rights over the database: Admin
As long as Admin has no password, you don't get the logon screen. The logon dialog appears when you set a password for Admin.
In your case Admin keeps full rights over the database and you're distributing the application to users that have the original Access system file (user Admin authenticated without password). That's why the database 'forgets' all security.
To enforce maximum security on the database, you have to remove the generic user Admin from Admins group (or delete it entirely). I also suppose that the owner of all objects is also Admin. If this is the case, change the owner.
If you do so, you'll have either to distribute the 'system.mdw' file to the users or recreate the accounts on their workstation, because they will not be able to access the database (trying to logon as non-existant user Admin).
Do not forget the user names, passwords and PIDs, especially for the user(s) with administrative rights. Otherwise you may lose all your work.
Keep in mind that securing a database is NOT a simple thing!