Actionscript
Somewhere in your main loop:
if (image.x == (0- image.width))
{
image.x = stage.width;
}
In the last frame where it disappears:
goto (frame x); //where x is frame where it appears, but your entire movie will rewind
Or:
image.x = stage.width; //if you only want the image location to be resetted
*note - I'm not sure if this is the exact syntax, been a couple years since I have touched Actionscript (for Flash 5 and 6). However, hopefully this will lead you in the right direction.
Edit 2-
Now that I think about it, Flash will repeat itself at the end of the movie unless you tell it not to. So you might have your effect already (may it be good or bad, since your entire movie will repeat). You also may just want to make it modulized, like having your background be another repeating swf that is loaded into the main movie.