Well, one possible way would be to dig through the HTML and find the url of the video which is actually playing.
To do this:
Start your browser, go to the page as normal, and then go to View > Source (or something similar). It should pop up a text editor with a lot of HTML. Search for the text '<object' or '<embed' and look past that till you get to the SRC= attribute. (These are the start of HTML code that tell the browser the page wants to 'embed' an active object in the page, for example the video player).
For example you might see
<object name="something" src="/some/path/here/to/the/video.wmv" ....
Take the stuff inside the src= part (the path) and put it onto the URL in the address bar. If it starts with a slash (/) remove everything except the domain name (so if the site is for example,
http://members.whatever.com/members/video.html, remove everything after .com and paste the SRC you got there. If it doesn't start with a slash, remove everything after the last slash in the URL and paste the src there.
Browse to the newly formed URL. If all goes well, you *should* be looking at the file directly in the web browser, without the extra page content that surrounds it. You should now be able to use the save feature of your browser (File > Save or something similar) to save the file to your computer.
I hope this explains it clearly enough If you need any help, feel free to ask!
By the way, if you use Firefox and have the Greasemonkey extension, you might be able to find a Greasemonkey script for the site that can add links which will automatically save the video on the page for you. (I know such scripts exist for sites like YouTube which have no save feature directly on the page).