The phrase "a constant headache for" is correct and usable in written English.
It can be used to describe a situation or person that consistently causes annoyance or difficulty.
Example: "The ongoing technical issues have become a constant headache for the IT department."
Alternatives: "a persistent nuisance for" or "a continual source of frustration for".
"CHURNING" is a constant headache for the companies that provide Internet access.
He said he had a constant headache for the first month.
Flight delays are a constant headache for business travelers, who are the airlines' most lucrative source of revenue.
President Clinton's engagement policy toward North Korea was a constant headache, for Kim Jong Il was brutally repressive and tried to start a secret uranium program.
Large-scale protests and riots among farmers, unpaid migrant workers and laid-off laborers in rust-belt cities have become a constant headache for the government, even as the economy grows at what many economists consider an unsustainably robust pace.
The way things look now, a shift in focus to Justice Verniero, the former attorney general who was appointed to the state Supreme Court in 1999, will only replace a constant headache for Mr. DiFrancesco with a serious pain in the neck.
"We're terrified," said bus driver Rodrigo as he started his engine, complaining of a constant headache from the strain of checking over each passenger and keeping an eye out for suspicious behaviour.
Since taking office, he's been a near constant headache for the White House a polarizing and politically tone-deaf dud at the center of almost every controversy the president faced during his first term.
But the inquiry has been an almost constant headache for Mrs May.
Since the paintings were discovered by four teenagers (and a dog) in September 1940, however, their preservation has been a constant headache, with government officials in Paris and the local authorities criticized for failing to ensure their proper protection.
And it was a constant headache in developing a new personnel system, Nycaps, as agencies sparred and consultants clamored for mayoral intervention.
