I ran into this japanese medical site. http://www.kojinkai.or.jp/msc/outpatient-selfcheck18.html
The title "意識が遠くなる" stumps me. Best I can guess is "Consciousness is fading." Is that right? "Consciousness becomes far." sounds weird.
The literal translation is indeed "consciousness becomes far". It's a set phrase meaning "to have lightheadedness", "to have the feeling of faintness/blackout", "to almost faint", "to be half-unconscious", etc. There is also 気が遠くなる, which means almost the same thing but has an additional figurative meaning.
