So, if I have this down correctly:
He had surgery for ptosis, which has not completely corrected the problem, but yet the eye does not close completely when asleep?
Assuming the sleep situation is secondary to surgery I would be hesitant to do a second right away. You don't want the cornea getting too dry during the night as it could then predispose him to infections in that eye.
Having said that, I am an optometrist, not an ophthalmologist so would be interested to hear the surgeon's opinion. Does s/he thing that the lagophthalmos (open when sleeping) would also correct with a second surgery?