Fewer people who test positive for the coronavirus are answering calls from Carmarthenshire Council's test, trace and protect (TTP) team, prompting a warning from leaders.
Last week, the team could not get through to 11% of the 337 positive cases despite calling them more than once.
Jonathan Morgan, Carmarthenshire's head of homes and safer communities, told a council committee: "It is getting more difficult. There is some fatigue setting in.
"We are seeing a bit of complacency."
He said the successful contact figures were still very good, but had dropped from a couple of months ago.
Asked by Cllr Karen Davies if he felt that positive cases were giving the TTP team the "full picture" as to their recent contacts, Mr Morgan replied: "It varies. Some are absolutely open.
"Others will say they have not been in contact with anybody, or very few.
"It's a mixed bunch, if I'm honest."
Councils, in conjunction with health boards, set up TTP teams to reduce the spread of Covid-19.
People who test positive are required to share details of people they live with and those have been close to up to days days before their symptoms started.
These contacts are informed they must self-isolate for 14 days to ensure they do not have the virus.
The council's TTP team has more than 30 staff and operates in the public protection department.
Cllr Philip Hughes, executive board member for public protection, said: "I would like to reiterate the need for everyone to adhere to the Covid regulations.
"They are there for a reason. The vaccines are encouraging but we are not out of the woods yet.
"I cannot stress enough the need to follow the rules."
Cllr Dorian Phillips said he believed workers were deterred from self-isolating if they only received reduced sick pay during the 14 days of isolation.
The situation could be different, he said, if they received 80% of their wages as per the furlough scheme.
Cllr Phillips said one of his employees who tested positive for the coronavirus got himself tested again after the self-isolation period because he didn't feel quite right.
He said the employee ended up testing positive three times and stayed away from work, but in theory could have returned sooner and potentially spread the virus.
"He did it out of his own goodwill," said Cllr Phillips. "How many others are out there who are still positive?"
Mr Morgan said people could test positive again after 14 days, but might not necessarily be infectious at that later point.
Cllr Phillips said: "Everybody should have a test before they are allowed back to work."
Mr Morgan and Cllr Hughes said Cllr Phillips had made good points, and that they would be forwarded to Public Health Wales for consideration.
Mr Morgan also said that rapid tests - known as lateral flow tests - which yielded accurate results after 30 minutes would be a "game changer".