Disclaimer: I've searched for the answer of this question quite extensively online but I never got anything 100% reliable. The best I got was the answer a friend gave me because his friends has done this (open Dark Grounds during Rapid Respawn). So, take what I will say with a grain of salt. It has not been proved nor verified, but I doubt you will find such thing online.
To open Dark Grounds the server has to collectively complete the task Mend What's Broken 80 times throughout as many server saves are need.
I have no information about how long it stays open (if a single or multiple server saves) and if there's anything that can be done to keep it open or to close it.
The correct answer is: Mend What's Broken is not the task to open Dark Grounds
This 7 year long mistery has finally been solved, thanks to the player Brighid Grand Explorateur from Gentebra. There was a popular belief (myself included) that the task Mend What's Broken was needed to open Drak Grounds, but the answer lies in another task given by the Dream Butterfly. The report of this finding can be found here. There's also an interview with the player. Unfortunately, I believe it's only available in Portuguese.
To open Dark Grounds area, 20 Soothing Bad Dreams tasks must be completed. This task is also given by the Dream Butterfly but it's not necessary to get the Dream Warden outfit, hence the reason the area was so rarely open. According with the Brighid Grand Explorateur interview, theses tasks don't have to be completed in the same Server Save cycle, since he found this out by doing the task twice per day.
After that, a ladder will appear nort of the Roshamuul depot and it gives access to the Dark Grounds. The area will remain open for 15 to 25 days, depending on more tasks being completed.