Going by past years, probably around November, if they even continue doing them. Judging by the annual survey, they want to change how double XP weekends work so players aren't getting direct xp boosts for free, and instead get them from alternative methods...
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Success is not final, failure is not fatal. It is the courage to continue that counts.
FiFiáLaFelessaid: Soon, I hope. I also hope they don't change the format to something complicated and annoying. Or worse, you have to buy stuff to qualify (don't even think about it, Jagex, it would never work).
They already pulled a similar ruse with Vic (used to always be free for everyone, now held hostage behind a paywall), so I wouldn't be surprised if they tried it with dxp weekends as well. I mean, psychologically it makes sense: people are used to dxp weekends as they are now, that having to live without them would be too difficult for some, manipulating them into paying extra to qualify for future dxp weekends (akin to the "free taste" of addictions like drugs, gambling etc). Inhuman to take advantage of it, but there it is.
"These ghastly beasts CAN be slain! They CAN be overcome!" -Borch Three Jackdaws