'constant complaints' is correct and usable in written English.
You can use 'constant complaints' when describing a situation where someone is consistently unhappy or dissatisfied. For example, "The employee had a history of constant complaints about her colleagues."
And, after constant complaints by Republicans, Obama has finally stopped blaming Bush for the poor economy.
Isn't it one of the constant complaints about politicians that they promise things and never deliver.
She had been very impatient with her women friends' constant complaints about unreliable servants, bad marriages, worse divorces.
Doctors who cared for her in various hospitals had grown weary of her constant complaints and started giving her morphine.
There are constant complaints today that politicians are 'out of touch', that they refuse to listen to the electorate.
In a September 2007 cable the embassy reports hearing "constant complaints of shortages of materials, qualified workers, and infrastructure".
Aware of the constant complaints, the central government had thought of replacing the hot food with prepackaged meals.
And it is isolating: Family members and friends may lose patience with the constant complaints of pain sufferers.
Medical service department has received constant complaints from workers assigned to this workstation, which reported mostly musculoskeletal discomfort in shoulders, neck and back.
Mr. Baird, who is retiring in September, reserved his harshest comments for corruption, the theme of constant complaints by foreign businesses here.
In Washington, one family fended off constant complaints from a next-door neighbor during a renovation, even as the contractors lowered the noise level and shortened work hours.
