"continual attempts" is correct and usable in written English.
You can use it to describe someone who is making several attempts at a task, perhaps over a period of time, or without ceasing. For example, "Despite his continual attempts, he could not get the door open."
Moreover, there have been continual attempts to impose a political unity over the region.
The movie is as repetitive as hell and, despite his continual attempts to raise the ante, quite boring.
During the latter half of the thirties he taught at Harvard, but often in menial positions: his continual attempts to get a tenured position there, at Cornell, at the University of California, and elsewhere were always foiled by circumstance, or, more often, by his erratic behavior.
The announcements are part of the country's largest phone company's continual attempts to capture market share in Internet services.
"As the pressure of the campaigns is mounting, so are the continual attempts to intimidate and subdue my support base," he said.
Even with the situation with Mr Haas there is a continual attempt to keep us away from him and a refusal to let us engage with him.
The public's discomfort with Mr. Obama has everything to do with his continual overreaching attempts to use ultraliberal solutions to deal with the nation's problems, and nothing to do with his race.
He pressures opponents with continual takedown attempts, wearing them down and doing damage on the ground.
Meanwhile, preliminary citizen-funded attempts to require recounts in Wisconsin, Michigan and Pennsylvania are under continual attack from well-funded Trump interventions.
Those systems are under continual attack.
It was supposed that a continual and prolonged attempt to reduce the core temperature added additional stress and reduced the survival rate [41].
