The phrase "a constant theme of" is correct and usable in written English.
It can be used to describe a recurring idea or motif in a piece of writing, art, or discussion.
Example: "In her novel, the author explores a constant theme of love and sacrifice throughout the characters' journeys."
Alternatives: "a recurring motif of" or "an ongoing theme of".
The latter quality is a constant theme of our conversation.
On the contrary, death is a constant theme of the early years of flight.
Transparency has been a constant theme of Francis's administration so far.
A constant theme of the year was the two main parties blaming each other for various failing NHS hospitals.
A constant theme of much of the recent research on finance and development is the importance of strong property rights.
(This was a constant theme of comic literature in the seventeenth and eighteenth centuries. Think of Molière, or "Tom Jones").
The importance of curbing income inequality was a constant theme for all of the candidates, and Sanders opened the night by calling the nation's campaign finance system "corrupt". All of these are signature Elizabeth Warren issues.
In the deep and sympathetic portrait "A Woman in Charge," Bernstein's recent biography of Clinton, a constant theme is her fear of humiliation; as the daughter of a harsh, often cruel father, she learned early to conceal any weakness and, ultimately, to protect her very humanity from exposure.
In Roth's work this is a constant theme, and one of the "systems" that sometimes gets it in the neck is feminism.
Relationship woes are a constant theme and source of inspiration for Longley but in concert, she sets them up in such a charming yet intimate manner that it's like she's sharing her deep secrets and true confessions with family and friends inside a heavily guarded circle of trust.
Like rebellion, the adoption of foreign elements has been a constant theme in the history of dress, and it too dates to antiquity.
