Hell David.

That's weird. In my Firefox, it remembers the last folder I saved files in, as it did in yours. Well, it's possible that you are having a problem with some Firefox add-on that is hindering your Firefox's normal behavior. Have you tried disabling all add-ons (just to check), to see if Firefox goes back to normal?

Whenever you have a problem with Firefox, whatever it is, you should make sure it's not caused by one (or more than one) of your installed add-ons, be it an extension, a theme or a plugin. To do that easily and cleanly, run Firefox in safe mode (don't forget to select Disable all add-ons when you start safe mode). If the problem disappears, you know it's from an add-on. Disable them all in normal mode, and enable them one at a time until you find the source of the problem. See this article for information about troubleshooting extensions and theme and this one for plugins.

If you need support for one of your add-ons, you'll have to contact its author.

Thanks for the suggestion Morbus, but unfortunately that did not do the trick. The problem remains the same when I start in Safe Mode and disable add-ons.

Please do this:

1. go into Help > Troubleshooting Information...
2. click Open Containing Folder
3. close Firefox
4. in the folder that opened in point 2, rename the file downloads.sqlite into downloads.sqlite.bak
5. open Firefox

Now your downloads will hopefully remember where you saved them. Of course, your download history will be in the downloads.sqlite, which, if doing this works, is corrupt and should not be used. You can restore it back, if you want. Or delete it.

that didn't do it either. The problem remains the same on every Firefox startup.

Thank you for all the help so far though, I appreciate it!

Very weird... Ok, please create a new temporary Firefox profile. This is just for diagnostic purposes: managing profiles. See if the new profile has the same problem.

Okay, we're getting somewhere now! The new profile doesn't have the problem at all. I've switched back and forth, and my current profile still has it, but the other does not - and works as normal.

On the safe mode test, my add-ons didn't seem to be an issue, so I'm not sure where to go from here.

Well, from what I can see from your info on the original post, I believe there's a config preference that's causing this. But I may be wrong. Do this:

1. access about:config in your location bar
2. if the browser asks you something, say "yes whatever" or whatever appears :P
3. in the page that appears (the about:config page) search for privacy.sanitize.sanitizeOnShutdown
4. set that entry to false
5. restart the browser

I'm hoping this will do it, because I'm not seeing any other possibility. But if it doesn't, please tell me and we'll manage a way of porting your own profile into a new one and circumvent this problem. I hope it won't be necessary though :)