The phrase "continually in search of" is grammatically correct and commonly used in written English.
You can use it to describe someone who is constantly seeking something, whether it be physical or abstract. Example: John was continually in search of new adventures and experiences, always eager to explore new places and meet new people.
Early humans were almost surely hunters and gatherers who moved continually in search of food supplies.
The Reasoner himself is a speaker continually in search of understanding through the application of reason to experience and observation.
The term "silver linings" is Pat's therapy mantra – he's continually in search of "positivity" (the Playbook part is presumably a residue from Matthew Quick's novel).
Something of the same effect was produced at Merkin, a staid but comfortable 450-seat Kaufman Center space continually in search of identity, as performers trooped across the stage in more or less efficient succession.
The New Yorker, September 13 , 1999P. 106 Briefly Noted review of "The Vandals" (BOA Editions; $12.50) by Alan Michael Parker...In [t]hese interconnected poems...Parker suggests that the vandals' qualities are not unlike those of poetry itself, which is continually in search of something new; his musical and witty poems respond eloquently to that desire.
Some hipsters do this with a greater sense of irony than others -- irony, because, in seizing on something authentic and making it popular and hipster, they might be making that thing "inauthentic" again, like tourists continually in search of remote vacation spots that haven't yet been touched by tourists.
It wasn't just Idina but many of her spouses, friends and acquaintances who seemed to think little of abandoning children, jettisoning mates and continually moving on in search of new lives or new adventures.
Los Angeles is home to a cadre of independent artists, producers, DJs and promoters that continually challenge the status quo in search of their own vision.
However, Mansour never intended to continually fork out millions upon millions in search of ongoing success and, from the very beginning, City's long-term strategy has been to sustain their position at European football's top table by focusing heavily on developing their own talent.
New technologies continually arise, offering repeated opportunities to artists in search of the technologically novel.
The number of customers who fit that description is increasing rapidly, too: the advent and growth in popularity of cloud services means that big companies like Facebook, Apple and Amazon are continually building and expanding new data centers in search of greater storage capacity.
