I don't have any details, but its possible that the biologists have candled the eggs and know that they have failed and have removed them. The eggs would keep the male trying to incubate - projects used to use dummy eggs to keep birds on nests for short periods of time until chicks or fertilized eggs could be substituted.
And reading the original note posted here, it didn't say he abandonned the site (or am I missing a later note?) but rather that he left the nestbox. If the eggs aren't there, he won't be either.
As for turning the cam off, if the birds aren't there, there really is no point in leaving it on. The male might or might not come back. If another female were to turn up and he should try to renest, the equipment is still there. If he doesn't find a new mate, he could stick to the territory or he could take off to better feeding areas in a while.
We could hear more about the situation later or a new lady will arrive and we get to start from the beginning again ...