"continuous challenge" is a correct and usable phrase in written English.
You can use it to refer to an ongoing situation that is difficult to deal with or overcome. For example, "The continuous challenge of providing quality education to children in underserved communities is one that many organizations strive to meet."
The emergence of surface mutants however is a continuous challenge to design more effective immunoassays.
Soil tillage interaction presents a continuous challenge for researchers, developers and manufacturers.
In computational biology, the continuous challenge is to manage the biological data.
The complexity of this transport machinery makes investigation of processes such as tubular drug secretion a continuous challenge for researchers.
The ongoing increase of nutrition-related diseases is a continuous challenge in the development or improvement of foods.
However, a continuous challenge remained in the field: technical limitations in high-throughput screening and precise manipulation of strains.
However, low thermal conductivities of organic PCMs have posed a continuous challenge in its large scale deployment.
Strong surface adhesive forces between neighboring surfaces in nanoelectromechanical (NEM) switches have presented a continuous challenge to the fabrication and operation of these devices.
Confusion and concern about basic safety issues for disabled drivers is a continuous challenge for the mobility industry, which is trying to promote quality standards after decades of improvisation.
Finding good teachers is a continuous challenge, she said, and she harbors plans for a junior-year-abroad program, so dance students from American colleges can come to her school and earn college credit.
Providing an evidence-driven infrastructure is critical to addressing the continuous challenge of managing effective nurse-patient assignments in a workable staffing plan.
