Which Downloads folder are you referring to?
If it's the one in the bleow path, then there really should be more than just the minitri file in there. Even with the purging enabled, the LUA always keeps the latest defs. If there's nothing in there, then the LUA isn't downloading from the sounds of it.
<ProgramData>\Symantec\LiveUpdate Administrator\Downloads
On another note, I don't recall if I mentioned it in your other thread, but it not recommended to have both the LUA and the SEPM on the same box, which your last post seems to suggest they might be:
http://www.symantec.com/docs/TECH93409
If they are on the same box, and if the LUA is not downloading anything anyway, then you may wish to consider removing it.