WHY DOES IT SHUT OFF?
I haven't experienced this issue yet after about a month and a half with the two 4600's we have (although we don't use power save mode). I have seen a few posts about other LG phones displaying this issue as well but had not seen the power save explanation. Interesting.
Try going into your "Power Save" settings ( * under "Display"), set it to "Always ON" and see if that cures the problem.
Menu -> 8 (Settings) -> 2 (Display) -> * (Power Save) -> Always ON (meaning the power is always on)