"perpetual quest" is correct and usable in written English.
You can use it to refer to a continuing attempt to find something or to seek knowledge or understanding that never ends. For example: He was on a perpetual quest to unlock the mysteries of the universe.
"I'm on a perpetual quest for air-conditioning," she said.
But officials said that given the authority's perpetual quest for revenue streams, the option could not be overlooked.
They also are in search of Eeyore's tail, and Pooh himself, true to form, is on a perpetual quest for honey.
Sports gamblers everywhere unite in the perpetual quest to find an edge, and never more so than when they bet on the N.F.L.
Yet audiences seem to like shows built on a perpetual quest for a relative's killer, a template that goes back to "The Fugitive".
Morey has repeatedly acquired and flipped high-value players and draft picks, reshuffling the roster in a perpetual quest to put the Rockets in position to make a blockbuster trade.
This dramatic transition has apparently left her with an eternal quest for a sense of belonging and a perpetual cultural identity crisis.
Danilowitz notes the mismatch between the perpetual Jewish quest for safety, protection and acceptance, and Israel's stance on gay marriage.
Together, the two new sections will bring in $4 million to $6 million this year, a considerable sum in Boston's perpetual, and usually futile, quest to outdo the Yankees.
Lone rangers, from Don Quixote to Sam Spade and James Bond, are customarily engaged in combat against bad guys; they afford themselves the escapism of a virtuous quest, a perpetual cleanup.
And yet, oblivious to the logic that atheism cannot be any more epistemologically verifiable than theism, the shortsighted Modernist could see in religion only the causes of factionalism, persecution and perpetual warfare, not the quest for the authenticity and benevolence at the heart of society.
