The part of the sentence "face increasing challenge" is correct and can be used in written English.
You can use it to refer to a situation in which somebody is presented with increasing difficulties that need to be addressed. For example, "The company has been able to face increasing challenge thanks to its highly skilled staff".
"Aspiring lawyers face increasing challenges in accessing the profession.
Still, the trams face increasing challenges from the well-financed M.T.R., which is expanding its reach around Hong Kong Island with a new line to the southwest coast, while extending its main Island Line to an area where the tram now faces no underground competition.
Once GTA IV ships, Take-Two will again be dependent on less-popular titles and face increasing challenges to compete with larger and better-capitalized competitors.
Water resource managers face increasing challenges in identifying what physical and chemical stressors are responsible for the alteration of biological conditions in streams.
Armed with potentially limited communication and computational resources, designers of distributed imaging systems face increasing challenges in the quest to acquire, compress, and communicate ever richer and higher-resolution image ensembles.
Farm businesses face increasing challenges in the face of policy reform which envisages multifunctional rural economies with objectives which span the environmental, the social as well as the production of food.
Forests also face increasing challenges.
Without new creative and collaborative approaches, our national parks will face increasing challenges to maintaining the quality of park facilities and ranger services, and will struggle to protect the resources that preserve America's heritage.
Low- and middle-income countries (LMICs) face increasing challenges due to incorporation, diffusion and utilization of new and modern HTs.
Health services around the world face increasing challenges in matching the demand for needed skills with supply [ 1- 3].
