@The-Question It seems that you cannot complete multiple runs of one those Urgent Quests and have it count toward unlocking the special rewards as denoted at this URL in the red text: "only one completion per time slot will count towards the Special Rewards". That is why I was concerned, because if you missed one day of the beta due to personal reasons or work, there were not enough Urgent Quests to complete on Sunday with the schedule they had setup.

https://pso2.com/news/announcements/cbtrewards

Will there be another time for us to unlock the closed beta urgent quest awards(like in an open beta)? It seems that there are only 2 urgent quests left before its over and they take place really late today for East Coast people, and I worry I wont be able to complete them due to my work schedule tonight and tomorrow morning. This community is wonderful and thank you guys for always providing great info on these forums!