[raymo]

I have a 600D but have never tried connecting to a TV.
Mine attached to my scope and made videos o.k.
The "Attach a lens" message does not stop you making a video, if you don't
attach a lens [or scope], it just videos a blur.
LiveView should remain on whether shooting stills or video.
Does the LV shut down after 30secs when connected to just the scope, or
only when connected to the TV as well.
If it does it when only connected to the scope, something is obviously wrong.
I assume that there is plenty of life in your battery. If only when connected to the TV, then I have no idea, maybe somebody else can help you.
raymo