I had this issue too, They're right on the money about the power supply...
Its not your Fuel life (indef is what I usually get too, Thank The Programmers for Bussard Ram Scoops), Its your Capacator level.
Those Mining lasers take a lot of capactor power, And if that power for any reason hits 0, the entire ship shuts down and goes adrift. I think we attribute it to Life Support failing most of the time (I never use Computers, Perfer to take those points for other bonuses), But in your case, Imagine your spaceship just pulled a hard reset due to lack of battery power.
Try adding a capacator to the ship, Something small like .25 or so will probably be enough to avoid spontainious shutdowns.