"have continuously sought" is grammatically correct and can be used in written English.
It is used to describe an action that has been ongoing or persistent over a period of time. Example: The researchers have continuously sought answers to the question of climate change for the past decade.
Livingstone says that photographers have continuously sought him out to tell him how tough the industry is and how unfavorable the terms are for artists on most digital photography sites.
In the end, a Commission was envisioned, but some have continuously sought to suffocate it by choking funding, a small commitment compared to the cost of myriad layers of unnecessary political institutions that feed nationalist patronage and crony capitalism.
Studies in bioconversions have continuously sought the development of processing strategies to overcome the "close physical association" between plant cell wall polymers thought to significantly contribute to biomass recalcitrance [Adv Space Res 18 :251996], 1996],[ Science 315 :804–807, 2007].
"The only beneficiary of the EPA's decision is Big Oil, which has continuously sought to undermine the development of clean, renewable fuels.
After 16 years of fighting between Morocco and the Polisario Front, which has continuously sought to gain independence, the situation peaked in 1991 when the two sides finally signed a UN-brokered ceasefire and the peacekeeping mission known as MINURSO was established.
The remaining state-recognized tribes that are seeking federal recognition have continuously maintained their reservations and their government to government relationship with the state of Connecticut, Ms. DeMarce noted.
He was right in the sense that most of the better artists have continuously searched to explore the possibilities and seek to break the boundaries of particular forms.
Federal courts have continuously struck down the most egregious legislation.
The firm's revenues have continuously expanded.
They have continuously built new and expanded existing settlements.
Despite improvements in conventional cancer treatment the prevalence of cancer-related deaths has minimally changed and novel therapeutic strategies are continuously sought.
