Yes, he can still drive, though he must get a medical clearance to do so from his main diabetes doctor. She will want to uncover why he's having repeated hypoglycemia
episodes and figure out a way to deal with these situations. The doctor will also want to discuss safety measures your father needs to put in place to protect himself and others when he's on the road.
To begin with, your dad needs to test his blood sugar before he gets behind the wheel, and, if he discovers it's low, he should have a snack before he even thinks about picking up his car keys. He should also keep a stash of glucose tablets in the car for an emergency situation. He should leave them in a place, such as the glove box, where they can stand the wear and tear of temperature extremes within a car.
He needs to bring his blood glucose meter with him as well, and he should pull over if he experiences any low blood sugar symptoms, such as sweating, trembling, feeling irritable or anxious, fatigue, thirst, shakiness, or hunger. If he forgets his meter, he should respond to such symptoms as if he's low and treat himself accordingly -- with glucose tablets or a snack. Your dad shouldn't try to continue driving if he thinks he's having a hypoglycemia attack. He should pull to the side of the road as quickly and safely as he can and treat his symptoms or call for help.
If your dad is planning a long drive, he should take extra precautions. He should test his blood glucose about every two hours during a road trip to make sure it's in his recommended range. He should also pack extra food, drinks, and hypoglycemia remedies in a handy place so they're readily available when he needs them.
From a legal standpoint, you and your dad should know that if he treats his diabetes with lifestyle changes -- by healthy eating and physical activity -- then he doesn't need to inform his state's Department of Motor Vehicles (DMV) about his diabetes. If, however, he takes diabetes pills or insulin to treat his disease, he needs to notify both his DMV and his insurance company.