I filed a ticket about this quest today, because I dropped it on an alt thinking that it was bugged...and when I did, it was not offered to me again. I received it yesterday but did not get around to travelling to Light's Purchase until today.
Here was the CS response:
Just dropping by to talk a little about the quest "Reinforce Light's Purchase". There isn't much details in-game explaining the Light's Purchase area along with the Veiled Den area, but these two places alternate. It looks like Light's Purchase was active yesterday and if the quest wasn't completed yesterday it will appear later down the road! There isn't anything tied specifically to this quest so I can assure you nothing was missed. It mainly just leads you to a location to see in Antoran Wastes, kind of like Reinforce Veiled Den did.
Within the next couple days Light's Purchase should appear again and you'll be able to complete the quest like normal. The quest wouldn't work if the quest was picked up on the active day and then attempted to complete on the inactive day because Alleria Windrunner would not be at that location.
There is no rep requirement for the quest, per CS. I can confirm this because my Pally was not Honored with the Army of Light and had no issue completing it...but I got it yesterday on him and also completed it on the same day.
Hope this helps someone who was confused like I was and saves you from wasting an hour trying different things (as I also did) :)