"unceasing fight" is a correct and usable phrase in written English.
You can use it to describe a situation where a person or group of people is struggling without rest or respite. For example, "The athletes faced an unceasing fight to make it to the finish line."
Kennedy admits that security remains an unceasing fight.
He promised, in his inaugural speech, to wage an unceasing fight against the corruption that bedevils his country, and to assert the rule of law.
His administration, he added, will mark "the beginning of complete equality of the sexes, of the unceasing fight against criminal machismo".
Dr. Jacques Rogge, the I.O.C. president and a fellow Belgian, said, "His ideas and energy helped to begin an unceasing fight against doping and any activity damaging the integrity of the sport".
Allard K. Lowenstein, in full Allard Kenneth Lowenstein (born January 16 , 1929 Newark, New Jersey, U.S. died March 14 , 1980 New York, New York) American scholar, political activist, and diplomat who was known for his unceasing fight against injustice in many forms, evidenced by his participation in such causes as antiapartheid, civil rights, and antiwar protests.
These maneuvers may seem disjointed and experimental, but they're deliberate, and have helped broaden McGregor's sense of clarity amid the unceasing chaos of a UFC title fight.
When it comes to North Korea, unceasing readiness is the plan — a "fight tonight" attitude, as they say in the tightly knit US and South Korean command structure.
Their effort was unceasing.
Fighting between the Boers and British continued, however, until the resources of both Boer republics had been broken by unceasing strain against superior forces.
His effervescence is unceasing.
