I've been doing a little bit of work with video, and certainly don't have all
the answers, but these are just some thoughts

How are you telling the Media Playback component which FLV? Through the
Component Inspector or Actionscript? This might make a difference, but I have
no idea

Also is the FLV embed in the SWF or is it also being loaded dynamically? In
which case why don't you just have the media component in the original SWF and
dynamically load the FLV? or is there a reason? In this case you might even not
have to close the FLV, just hide the media component. This would allow for
quicker replay since the video would already be cached/buffered. Then you would
only need to close the video if another was going to be played. Maybe

Are you stopping the video before you unload the SWF? Or maybe during the
close sequence you could move the video playhad back to zero

Are you seeing these problems in the testing environment or through an html
page or over the internet? All of the above, none of the above