Firefox stores the last directory in which you saved a download. To clarify your question: you prefer to have Firefox ask you where to save, but you want the "last directory" cleared at shut down so the first suggested location is always the default folder, e.g., the Downloads folder? Or is it that you want to have the last directory remembered consistently rather on a site-by-site basis?

Regarding that second point, around the time of Firefox 7, the last download folder started being saved on a site-by-site basis. To turn that off, you can create a new Firefox preference named "browser.download.lastDir.savePerSite". Here's how:

about:config is an interface for changing Firefox preferences. To start it up, type or paste about:config in the location bar and press Enter. If you get a button asking you to promise to be careful, click it, and please be careful.

In the filter box, type lastdir and pause while Firefox filters the list.

Copy the following preference name to the clipboard: browser.download.lastDir.savePerSite

right-click the blank area and choose New > Boolean. Paste the preference name and click OK, then in the next dialog make sure false is highlighted and click OK again. You're done in about:config. Firefox should now revert to the earlier behavior of remembering one single last location.

Thank you jscher2000 You stated my question much more artfully than I did. I do indeed want the last directory cleared at shutdown so the first suggested location is the default folder, i.e. Downloads.Your suggested fix worked well, and I thank you. I am a little disappointed with Firefox that we had to go so deep into their program for this Fix. But I very much appreciate your expertise. Cheers.