Try this:
1/ Open up your Browser, and go to Internet Options.
2/ (I assume your using I.E)In the General Tab, Click on Settings for Temporary Internet files.
3/ Check to see how much space is reserved for the Folder, and also check the current location of the Temp Internet files.
4/ Go into Windows Explorer and go to the Temporary Interent Files, whatever that may be.
5/ Right Click on the folder and check the properties of it. If it has reached its level, or close to it, it will probably start purging files. Your video clip may be one of them.
6/ If this is indeed the case, then go back to the Interent Options and increase the amount of space. Or you could adopt better houskeeping practices and get rid of the temp files more often.
I have this problem occasionally when I download a clip, close the computer and come back again and the file is gone. I tend to cut and paste them to another directory.
You can also Right click on the clip's link and Save Target, and then specify where you want to save it to.
Hope this helps, but I would probably resign myself to the fact that the file is gone.
One other thing to try is go to Find and type in *.avi,*.mpeg, in the Named dialogue box. This will give you all files in a directory or hardrive, that have those extensions.