"persistent tension" is correct and usable in written English.
This phrase is used to describe a feeling or atmosphere of constant discomfort or unease. For example, "The persistent tension in the room made for an uncomfortable atmosphere."
His demands and his manner irked Churchill and Roosevelt and caused persistent tension.
What is most conspicuous is a persistent tension between college-trained sophistication and fictions of naïveté and personal authenticity.
The killings also came amid persistent tension in Gaza, where the Israeli army is continuing military operations to try to stop rocket fire into Israeli communities.
The possibility of Turkish troops' entering northern Iraq has been a source of persistent tension between the United States and Turkey.
In a poor country like China, there is persistent tension between wanting cleaner air and not having the money to pay for it.
There's a persistent tension between the firmness with which Harris commits herself to her catchphrases and the shallowness of her political commitments (and her record).
Chinese government controls on the region and Islam have become a source of persistent tensions.
The press secretary also denied that Obama could have done more to address the persistent tensions across the country.
The dispute hinted at continuing Russian espionage in the West, and the persistent tensions between Russia and the United States in the past several years.
China's investigations of multinationals, persistent tensions with neighboring countries and surging blue-collar wages have prompted many companies to start looking elsewhere for large labor forces.
What we see across all of these cases is that in every country there are persistent tensions between social-welfare provisions and issues of immigration or ethnic division.
