We are having exactly the same issue. We thought at first it was related to the browser being used, but it happens in IE6, 7 and 8 and also Firefox, but strangely not Google Chrome. However, the company that supports our Moodle site, MoodleRooms, can not replicate the issue using any of these browsers.
The vidoes can be made to appear if the browser cache is cleared, but this needs to be done each time the page witht he videos embedd is displayed which is not practical in a school with 11-18 year old pupils.
I have also had this checked on other organisations networks with similar issues.
Could it be an issue that is related to the versions of browsers in different countries as all the testing we have done is in the UK and MoodelRooms are in the US?
A right-click on the non-dsplaying video shows 'Flash video player by Jeroenwijering' and Flash Player 10 details pop-up menu.
Our code is similar to that shown above :-
<a href="http://grange.mrooms2.net/file.php/608/8ry-STEM3_-_The_Digestive_Process.flv">A video about 'THE DIGESTIVE PROCESS' taken from Youtube</a><span class="mediaplugin mediaplugin_flv" id="filter_flv_12650986191">(Flash video)</span>
var FO =
width:"480", height:"360", majorversion:"6", build:"40",
allowscriptaccess:"never", quality: "high", allowfullscreen: "true" }
I have found that using the following html code the videos ALWAYS display. I may not be easy to get new users to Moodle to use this code. Edit the http lines that point to the URL or your Moodel video player and the FLV file you wish displayed. The height and width lines can also be changed to the size of video display window required.
src="http://YOUR MOODLE ADDRESS/filter/mediaplugin/flvplayer.swf"
flashvars="height=320&width=400&file=http://INSERT URL OF YOUR VIDEO HERE.flv"