This happened to me for this first time this week as well, on this character - my main.
What I noticed - I did 3 of the weeklies before realizing they weren’t dropping. I then head to the forums where I notice a post, with someone who has the same problem:
I noticed after a certain point in time people started to say they had no issue - it seemed like about 3-6 hours after RESET! The main takeaway was that it seemed time dependent, with most of the issues coming from closer to the reset time.
A few hours after first noticing the issue, I decided to test it and see if the comments were right, since I hadn’t actually logged out yet since coming on from the reset. I logged out, logged back in, finished my last weekly quest and got my one remaining key…
So what I would wager my guess on what is happening is one of two things, or some sort of combination - the reset is:
A) Not happening at the right time, its actually anywhere from an hour to a few hours after it is suppose to be (if you do them too quickly you are still on your lockout from previous week). Seems unlikely based on my experience
B) Not applying to players logged in too close to the reset time or were online during the reset application. I was able to get online 20 mins before the actual daily quest reset this week. Weekly reset (in EST) 10am, daily reset 11. I got on around 10:40-10:45am so the actual quests hadn’t reset yet, but I could go retrieve my GV.