Dozens of complaints about Milton Keynes Council were lodged with a local government watchdog last year, figures show.
The coronavirus pandemic has intensified existing problems, "widened cracks" and contributed to the most difficult time in several years for local authorities nationally, according to the Local Government and Social Care Ombudsman.
The body looks at complaints about councils and some other authorities, such as adult social care providers and education appeal panels.
Figures from the LGSCO show 53 complaints or enquiries about Milton Keynes Council were lodged in the year to March, though the ombudsman was closed to new complaints between March and June 2020.
That was down from 80 the year before.
The highest number of concerns (12) involved environmental services, public protection and regulation. There were nine cases related to adult social care.
Different data shows 25 cases deemed to warrant a full investigation by the LGSCO were concluded in 2020-21, with 17 resulting in a complaint being upheld against the council.
The reasons for the complaints were not provided.
Education and children's services were the subject of the largest proportion of complaints and enquiries nationally, with more than 2,300 lodged last year.
A further 1,700 related to planning and development while more than 1,600 were about adult social care.
At the height of the first lockdown, the ombudsman was closed to new cases and halted ongoing investigations.
Pandemic-related disruption contributed to a significant drop in complaints and enquiries across England, with 11,800 received – down from 17,000 the year before.
But the proportion of all cases upheld nationally has grown and was 67% in 2020-21, compared to 61% in 2019-20.
That proportion was even higher for adult social care complaints, at 72%, up from 69%.
Assessments and care planning were the most common areas of complaint in relation to adult social care.
Michael King, local government and social care ombudsman, said the figures showed investigators were finding fault more often.
He added: “While the way local authorities dealt with the pressures of Covid-19 is still being played out in our casework, early indications suggest it is only widening the cracks that were already there."
He said the concerns "cannot be wholly attributed to the trials of the pandemic."
The LGSCO said the growing percentage of upheld social care cases nationally reflected a “relentless rise” in the proportion of cases where care users and their families were let down by local services.
Mr King said the adult social care system was progressively failing to deliver for those who need it most.
A spokesman for the Local Government Association, which represents councils, said authorities and care providers had been doing all they could to keep "already severely stretched" services going throughout the pandemic.
He added: “It is right that providers continue to work with the ombudsman in its investigations, to make improvements to their services.
"We also need to apply the lessons learnt from our response to Covid-19 in any future reforms."
A Government spokesman said billions of pounds had been provided to local authorities to address pressures on their services throughout the pandemic, including specific adult social care funding.
He added the Government is committed to the delivery of "world-leading social care".