The phrase "maintain its popularity" is correct and usable in written English.
You could use it in a sentence such as, "The sitcom managed to maintain its popularity for over 10 seasons."
If "Ray Donovan" wants to maintain its popularity, and it is a very popular show, it needs to be all about Ray.
Mr. Sambora said that the band's professionalism helped it maintain its popularity.
Costco has long recognized that it must continue to hold that low-price position to maintain its popularity even if it means pressuring its margins from time to time.
Some observers of the fickle tween marketplace say they are surprised that "High School Musical" has been able to maintain its popularity as long as it has.
The Thai government had tried to maintain its popularity even in the last minute when it decided not to ask IMF for a rescue package immediately after the devaluation of the baht was announced, but waited until 26 days later to eventually called in the IMF.
If the game show can maintain its popularity, Ms. Sawyer can guarantee potential subjects extra-large audiences.
The 15th-century Renaissance in Italy witnessed the rise of a theatrical phenomenon that spread rapidly to France, to Germany, and to England, where it maintained its popularity into the 18th century.
Given that it has maintained its popularity and appeal hundreds of years later, it is one of the greatest books on personal responsibility and first-principles thinking.
Netball caught on in Britain and eventually gravitated to British colonies around the world, where it has maintained its popularity.
As a story, The Lion, the Witch and the Wardrobe maintains its popularity because it is a classic battle between good and evil.
Whisper is arguably maintaining its popularity today because it has veered into "adult" territory thanks to its "NSFW" category and other sexual content.
