The phrase "continuously faced" is correct and usable in written English.
You can use it to indicate that something is happening repeatedly over a period of time. For example: "Students in the class were continuously faced with challenging test questions."
"These were major emergencies we were continuously faced with," she said.
The available test methods are continuously faced with many new demands for engineered surfaces; this arises from reducing film thicknesses, more complicated film composition, and extreme mechanical requirements such as high hardness, stiffness and adhesion.
From small decisions -- "Should I get the passion fruit or the mango sorbet?" -- to more serious ones, "Should I break it off with Brendan, or wait until he gets a job?" -- we're continuously faced with choices.
Man is continuously faced with several lethal infectious diseases caused by pathogenic microorganisms [ 1].
Biological systems are continuously faced with variability generated by both internal and external sources.
Being HIV positive, Tamara continuously faced discrimination before coming to the centre.
Engineers in industrial and control sector continuously face problems on developing modern distributed industrial control applications.
Chemical processes are continuously facing challenges from the demands of the global market related to economics, environment and social issues.
Atop a monument called the Neutrality Arch, a gold statue in his likeness one of the many such statues and portraits scattered throughout the country was designed to rotate to continuously face the Sun.
Due to the current financial constraints in power industry, power plant operators are continuously facing a wide range of challenges when dealing with maintenance scheduling and asset management practices of the plant sub-systems.
Companies are continuously facing the resistance to settle into the ever changing technological environment.
