What is the download location (folder) on your hard drive?

Are there still files in that folder?
There should be a .part file with the specified name.

It is possible that cleanup software or anti-virus software has removed the files or that they were still in the temp folder when you paused them.

Hi cor-el:

  感谢阁下忙中偷闲及时回复指教，
  下载文件夹的位置是 firefox 指定预设的，我没有另外设置，下载时那个文件夹里有2个图标，一个是压缩包，另一个像一页信纸，我点击“暂停”后，压缩包的图标消失了。
  我是初级菜鸟，虽然您的指导很详细，对于其他网友可能一看就能心领神会，可是我还是解决不了暂停后继续下载的问题。再说除了在线视频以外，其他网站都没有断点再续的下载功能。
  我会加强学习历练的，再次深表感谢！

You're welcome.

It may not be possible to resume the download of a file if that file isn't seekable on the server.
In such a case you need to finish the download in one go without pausing.

Hi cor-el:

懂了，谢谢不厌其烦地指教，您真是个热心人。

You're welcome

You can try external download manager to see if that works.

• http://plugindoc.mozdev.org/windows4.html

You can integrate such DM in Firefox with this extension:

• FlashGot: https://addons.mozilla.org/firefox/addon/220