"continue its pursuit" is correct and usable in written English.
It is typically used to indicate that a certain action or goal is still being worked toward, despite any potential impediments or challenges the pursuit may face. For example: The company has faced numerous difficulties this year, but it is determined to continue its pursuit of industry leadership.
Purpose is like a freight train in that its momentum is too difficult to stop after it's started; it's too appealing not to continue its pursuit after that journey has begun.
Microsoft, which hopes Yahoo will help it compete more effectively against Google, is likely to continue its pursuit.
A member of the good government commission said the state would continue its pursuit of the shares.
But Novell pledged to continue a separate action and the EU promised to continue its pursuit of Microsoft.A potential clash of media titans loomed.
Thomas Welch, Shelton's corporation counsel, says the city does plan to continue its pursuit of the matter until Ms. Kusznir complies.
Mr. Zuckerman, who recently told his staff that his young daughter would be the next publisher of The Daily News, said he expected Newsday to continue its pursuit of Queens readers.
But in the unlikely event that the bankruptcy court rules in its favor, it has every intention of continuing its pursuit of Audible, said Mr. Springer, Digeo's general counsel.
While bolstering Mr Abbas, Israel yesterday continued its pursuit of those who take a harder line.
*** As the Emirates continues its pursuit of a western-style, Islamic modernity, the role of women is changing.
Despite Nixon's decision, Wildlife Services continues its pursuit, spending $140 million a year to kill coyotes and other "undesirable" animals.
The state-run news agency SANA said the army continued its pursuit of terrorists, as the government calls rebel fighters, in the Damascus suburb of Arbeen, inflicting casualties.
