"fading influence" is a correct and usable phrase in written English.
You could use it to refer to something that has diminished in importance or effect over time. For example, "The church had a fading influence on the local community as more and more people turned to secular lifestyles."
JEWS are a fading influence in north London, where almost half of Britain's Jewish population lives.
The rise of new and sophisticated constitutional courts elsewhere is one reason for the Supreme Court's fading influence, legal experts said.
The lack of fuss may be a sign of the financial weakness of the Standard, and the fading influence of the press generally.
Patrick Rishe writes on Forbes.com that his Livestrong Foundation has felt his fading influence and his financial woes will also begin to mount.
A more stable economy, based on the US dollar, coupled with Mugabe's fast fading influence, popularity and health, may mean that more decide it's time to come back.
What remained of the traditional media lacked the interest – because truth-telling is expensive and boring – or wherewithal – because they have no money, and fading influence – to effectively call out the lies spreading like algae over the warming western world.
His adversaries in Miami, while out of step with most Americans, managed to seize hold of the presidential campaign, bring the United States attorney general to their doorstep and reassert their once-fading influence on Capitol Hill.
Without proclaiming a presumptuously labeled policy such as "triangulation," "the Nixon Doctrine," or even a "freedom agenda," Obama has moved step-by-step to repair the damage caused by a plethora of Washington foreign policy debacles, old and new, and then maneuvered deftly to rebuild America's fading global influence.
Bernie Sanders and Elizabeth Warren have faded in influence this year; the ascendant senators Kirsten Gillibrand, Cory Booker, Kamala Harris, Chris Murphy, and Tim Kaine are closer to the Party's center.
But whereas Greek law faded in influence, the Greek legacy in the philosophy of law was to endure for several centuries, extending through the Middle Ages, during which there were many refinements and extensions of Greek themes and ideas, particularly within the Christian tradition.
While that's a genre label that he admits "could mean anything," especially as guitar rock fades in influence on pop, he saw the process as surprisingly validating about the Grammys as an institution.
