When you download files, Windows usually saves them in the Downloads folder, which is located under your user name in the Users folder on the drive where Windows is installed (for example C:\users\your name\downloads). When you are saving the file, you can choose to save it to a different folder. Some different types of files are saved to different folders by default. For example, if you right-click a picture on a webpage and then choose Save Picture As from the menu, the picture will be saved to the Pictures folder by default. If you're not sure where the file was saved, you can search for it from the Start menu.

if this not helped you see:

http://kb.mozillazine.org/Unable_to_save_or_download_files

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Some minor additions to the above:

To find where a file was actually saved, bring up the Downloads Manager window ("Ctrl+J"), and right-click on the download wanted then "Open Containing Folder".

The Downloads Manager window only shows where the file was saved, it does not get refreshed when the downloaded file is deleted.

An annoying change was also recently made where:

The Downloads window will close immediately when the download completes (starting in Firefox 4?), or not at all if the download is very fast. Use "Ctrl+J" to display downloads window at any time. To restore old behavior:

1. Click "Tools -> Options -> Main / Downloads" ("General / Downloads" starting in Firefox 3.6)
2. Uncheck "Close it when all downloads are finished".

Do the files only disappear from the Download Manager window or are they also removed from the hard drive?

For the first see:

• Tools > Options > Privacy > History: "Remember download history"

Also make sure that you do not run Firefox in permanent Private Browsing mode.

• https://support.mozilla.com/kb/Private+Browsing

If the later is the case then make sure that the files aren't removed by your anti-virus software or other cleanup software.

• http://kb.mozillazine.org/Unable_to_save_or_download_files