If you could have your high tech flier work for four days instead of two for the cost of the addition of a 35 cent photocell, wouldn't you add the photocell?
I'm just speculating, of course. I have no idea if there was a photocell included, here. My electronic knowledge is derived largely from the old 100-in-1 kit I had as a kid. But a photocell switch is pretty easy to make.
Throwies with one LED and an old motherboard battery have been reported to last up to two weeks. I don't know how battery energy scales from tiny Li batteries to big alkaline ones (though wiki has some ideas), but I suspect they had more than enough power to keep them running 24x7 for a couple of weeks.