Problem With Disk Image Password

This is related to another post I started regarding a problem with creating a blank disk image. I was able to create a new "disk image from folder" within Disk Utility. When I initially double-clicked on the disk image, I was asked for my newly-created password. No problem. However, when I subsequently tried to open the disk image again after I unmounted the disk image (i.e. tossing into the Trash), I was NOT asked for my password. Since I created the disk image to be able to password-protect a specific file, I need to be prompted for the password. Can you please help me sort out this problem? Thank you so much.