"continue relentlessly" is a correct and usable phrase in written English.
It means to continue with determination and persistence without giving up or slowing down. Example: Despite facing numerous setbacks, she continued relentlessly in her pursuit of becoming a doctor.
"But there is still an anti-Hull press that exists today within certain sections of the southern media and that will continue relentlessly.
"However, Afghanistan will continue relentlessly on the path that the people of this country have chosen: the path of peace, prosperity and reconstruction".
The airstrikes are expected to be a constant feature of the American operation and will continue relentlessly around the clock even as special forces come and go unpredictably.
We are living in times when educational pressures on families begin when children are toddlers and continue relentlessly through the teenage years.
These annual parties, which begin in mid-December and continue, relentlessly, through late January, are a longstanding Russian tradition in which children endure performances of various levels of vapidity, featuring Grandfather Frost and his granddaughter the Snowgirl.
As family members pass down their stories, each subsequent generation of Armenians continues, and will continue, relentlessly, irrespective of whatever political pressures Turkey may impose, to bear witness to these events and to demand recognition as genocide for what occurred.
Mr. Wilson's adding and eliminating continues relentlessly, the actors said.
The violence in Syria has since then continued relentlessly, with an ever rising body count.
The pigeon's de-vegetation campaign continues relentlessly and with a new intensity.
The flow of records inside the Water Cube continued relentlessly all day.
The attacks began as the nightly curfew lifted in Baghdad at 5 a.m. and continued relentlessly through the day.
