"continuous attempts" is correct and usable in written English.
You can use it to refer to a series of attempts that have been made over an unspecified period of time. For example: "Despite the team's continuous attempts, they were still unable to complete the project."
This stresses that the continuous attempts from the west to impose its values elsewhere are pointless.
"They broke into Baba Amr!" — after a month of the Syrian government's shelling, siege, and continuous attempts to invade Homs, this was expected.
Leaving aside its blunders in Afghanistan, Iraq, Libya and continuous attempts to portray China as a threat to its Asian neighbours, the western world's treatment of Iran is seen as nothing other than illogical and unfair.
Though the conservative regime succeeded in keeping the NSL intact, there have been continuous attempts to abolish or revise it.
In view of this, there have been continuous attempts to understand the complex three-dimensional turbulent two-phase flow.
The company said it "detected continuous attempts to login to AdGuard accounts from suspicious IP addresses which belong to various servers across the globe," in what appeared to be a credential stuffing attack.
Painting, he said, is "a continuous attempt at solving insoluble problems".
His continuous attempt to kidnap soldiers and the mortar bombs on Netzarim certainly endanger our civilians and soldiers".
There was not one word on the most extensive and continuous attempt to intrude into our computers, disrupt electronic infrastructure and steal technology and information.
Another characteristic of his speeches is the continuous attempt to reassure supporters that he has a coherent view of the world.
Dr. Callie Torres (Sara Ramirez) takes a leave of absence from the hospital, in a continuous attempt to bond with the grieving interns, who do not approve of her relationship with O'Malley.
