"there remain challenges" is a correct and usable phrase in written English.
It is often used when referring to ongoing obstacles to accomplishing a particular goal. For example, "Despite all our hard work, there remain challenges that must be addressed before we can reach our objectives."
Lead acid batteries represent a mature technology that currently dominates the battery market, however there remain challenges that may prevent their future use at the large scale.
While IoT allows for the gathering, processing and analysis of massive amounts of data from a broad range of sensors inside and outside the home, there remain challenges to presenting this data to consumers in a unified and intuitive way.
Despite this progress, there remain challenges that hinder efficient disaster health management in China.
While the introduction and use of bCPAP in this setting appears promising, there remain challenges in terms of guideline adherence.
But there remain challenges ahead.
Yet there remain challenges to the neighborhood's family-friendly image.
However, there still remain challenges for the day to day application of rationing decisions at health service (meso) level and at the level of the clinician (micro level).
While political commitment to the goal appears to be growing, in practice there remain many challenges.
In these additive approaches there remain significant challenges in preventing the nozzle from clogging during the deposition or the nanolithography tip becoming deformed.
Although progress has been made, there remain multiple challenges in the existing methods including the explosive number of possible failure modes, requiring correlation information, and excessive computational efforts.
To be clear, there remain important challenges to achieving sustainable forest management.
