"continues to cement" is a correct and usable phrase in written English.
You can use it when describing a situation that has been happening or is likely to happen for a period of time and is becoming stronger and more defined. For example: "As the company's reputation continues to cement itself among customers, they continue to gain more business."
The Yankees continued to cement their superiority; they lead Boston by eight games.
Well, that and because his one-out single in the seventh inning continued to cement his postseason reputation.
In remaining undefeated, Syracuse (17-0) contonued to cement itself as one of the dominant forces of the Big East.
The east Over in the east, Walter Schweppenstette continued to cement his position as my favourite villain by convincing his underling Hartmann to lie about the Nato report and make it look as though America was planning an all-out-nuclear attack.
Chairman Clive Leach said the support from the council and LEP would "continue to cement the North East's place on the international sporting map".
Last year saw YouTube continue to cement its position as the internet's go-to video portal, but a number of troubling incidents demonstrated the issues with unregulated content from new media creators and — now — bots that create content aimed at gaining clicks from children.
Hearables will only continue to cement their place as a major advancement in healthcare, as we continue to develop intuitive products and programs that further increase accessibility for the hearing impaired.
With the new addition of Lucy Liu to the cast as an officer with a video of a failed arrest gone viral on YouTube, this show is going to continue to cement itself as must see TV.
Nash continued to cement his reputation as one of the top footballers in the country, being called "the most versatile player in Australia", as, in addition to playing at centre half-back and centre half-forward, he successfully played in the ruck.
