Cannock Chase Hospital's Minor Injuries Unit closed in March 2020 so staff could be redeployed to help cope with the coronavirus crisis.
But now restrictions have been lifted, council chiefs in Cannock say it is time for the unit to be reopened.
They fear its continued closure will lead to more people heading to A&E at Wolverhampton's New Cross Hospital, heaping pressure on services. Both hospitals are run by the Royal Wolverhampton NHS Trust.
Hundreds of people have signed an online petition calling for the unit to reopen, while councillors said they had been inundated with calls from residents.
Trust bosses previously said they would be looking to reopen the unit in the summer but now say the situation "is under constant review".
Cannock Chase Council’s leader Olivia Lyons and health boss Val Jones have written to trust chief executive David Loughton to raise concerns.
They said councillors recognised the need to close the unit last year at the height of the pandemic but "many months on" and with the reopening of society they are receiving a growing number of complaints from residents about the unit and its services being unavailable.
They noted the "excellent reputation" of the Minor Injuries Unit and suggested its closure could put further pressure on the A&E and New Cross.
They said the unit has “served many in our community very well” but “are concerned that, as yet there appears to be no announcement of the opening”. They have requested a timeline for its reopening.
Mr Loughton previously said the pandemic had taken its toll on NHS staff, forcing many to take time off and resulting in the trust being stretched for resources.
Gwen Nuttall, chief operating officer at the Royal Wolverhampton NHS Trust, said: “The temporary closure of the Cannock Minor Injury Unit has been vital to provide enhanced support where it is clinically most needed – caring for seriously ill patients needing urgent care at New Cross Hospital.
"Like other NHS organisations across the region, the trust is seeing extremely high levels of emergency demand at New Cross Hospital and the extra staff have been vital to providing timely and high quality care. Together with Staffordshire commissioning colleagues, we will continue to keep the situation under constant review.”