Once upon a time there was a Firefox version which remembered where something was saved from a website. I think the last download destination directory was stored per host. I clearly remember that when I downloaded something from SourceForge, it would remember the directory, but since there are number of projects I download from it didn't always be a correct one. But for websites, I use for only one piece of software, it was always correct.
Then something changed. My Firefox wouldn't remember my destinations anymore.
Like the support forum promised, the configuration directive is hidden. They say hidden, but actually it is not created at all. Luckily you can add it by yourself by right clicking on the Firefox configuration:
Just add a new boolean variable with name browser.download.lastDir.savePerSite and you're good to go. Remember to set the value into true. It is enabled immediately, no restarting or anything needed.
The last thing for me to do is keep wondering why it was enabled in a couple of versions when it was introduced and then turned off.