When, if at all, does DL open up award tickets after the initial offering?

I've read quite a bit on award tickets and have benefited greatly from the advice offered on this forum (thanks to everyone for sharing).

So now I'm searching for first class low awards to LAX which appears to be the same as searching for the pot of gold at the end of the rainbow.

So I'm wondering after DL marks a set number of seats available for low awards when the flight is first listed on DL.com, does DL add any more low award seats to that flight at any point? If, for instance, it's wide open (lots of empty seats) would they add more award tickets or am I hoping against hope?