No, it does not turn itself off, The display goes dark is all.
On your computer you have a "Screen Saver" option, after so many mintues of inactivity (no input from user) the screen save kicks in.. IN days of old this was needed because CRT monitors could get "Burned in so they put on some animated thingy or another that prevented burn in.
ONE of the optional screen savers is "BLANK" (screen goes dark)
The Sensar Pro (And the manual actually explains this id you read it 3 times or more) does much the same thing, to conserve battery power if there is no user input (no buttons pushed) the display simply goes dark.. ONLY the display shuts off.. The unit is still functioning however when this happens. ONLY the display shuts off.
As I type this I am looking one that's about 2 years old.