Ubisoft Doesn't Plan to Remake Prince of Persia Games Other Than Sands of Time
Ubisoft has announced that at this time it has no plans to remake Prince of Persia games other than The Sands of Time. It also reiterated that it is still not ready to give a release date for The Sands of Time Remake.

Ubisoft Sands of Time, while taking a stance on the next remakes of Prince of Persia games. At this point the French company has no plans for other projects besides the refreshed version of the game currently under development.
This information does not seem particularly shocking. Prince of Persia: The Sands of Time Remake is being created in incredible pains. The project were met however, with a very cold reception, mainly due to poor visuals.
Eventually, the title have decided to withdraw preorders.
Of course, the fact that there are currently no plans to refresh the next Prince of Persia games, does not mean that in the future Ubisoft will not change its mind. Everything will depend on how The Sands of Time Remake sells. However, we will only find out about this in some time.