Unbeknownst to me, each time you type in the password, a drop-down add-on to the toolbar asks if you want to Remember the password, or Never for this site. It had never caught my before, as, on Netscape, it always came up in the middle of the screen, and you couldn't miss it.

Anyway, now that I clicked on Remember, the passwords appear in my Saved passwords section, so I believe I've solved the problem.

Don