The phrase "a continuing search for" is correct and usable in written English.
It can be used when discussing an ongoing effort to find or discover something, whether it be knowledge, solutions, or personal fulfillment.
Example: "The scientist is engaged in a continuing search for new treatments for the disease."
Alternatives: "an ongoing quest for" or "a persistent pursuit of".
Some microorganisms have become resistant to drugs, requiring a continuing search for different (and often more expensive) agents.
A letter laced with anthrax had arrived at the office of the Senate majority leader, Tom Daschle, leading to a continuing search for traces of the germs.
Coping has been hampered by a continuing search for answers and an unlikely series of wrenching events in the months after the shootings.
Others, though, see a continuing search for scapegoats as Washington uses more taxpayer money to cover bad bets by financial executives.
It gave an austerity to shows such as Jil Sander, Miu Miu and Dior Homme that became an important part of a continuing search for what's modern.
But regardless of the age of a fruit-growing industry, or the perfection of some of the selected varieties, a continuing search for new varieties is essential.
Not until 1940 did water shortages become critical, but since that date a continued search for new sources has been required to meet the city's growing demand.
More important, Thoreau's life, so fully expressed in his writing, has had a pervasive influence because it was an example of moral heroism and an example of the continuing search for a spiritual dimension in American life.
Its approval also served as a catalyst for the continuing search for better filler materials for the face.
The biggest potential bar to the move is Liverpool's continuing search for a forward.
That potential legacy looms even larger, given the Board of Education's continuing search for a permanent chancellor.
