As previously reported by the Telegraph & Argus, Tong Street Post Office in Holme Wood shut on October 21.
At the time, the Post Office said the branch had been " temporarily closed for operational reasons " - and that it was "working hard to restore service as soon as possible".
Tong Councillor Matt Edwards, who is leader of the Green Party group on Bradford Council, said he had made "repeated attempts to engage with Post Office Ltd" - but had received "only vague responses and no plan to reopen the existing branch or provide an alternative service".
He raised concerns that many residents have been forced to travel long distances for basic services such as withdrawing cash, posting parcels or accessing pensions and benefits.
Cllr Edwards said: "The Post Office is letting our community down.
"After almost two months, we still have no commitment to reopen the Tong Street branch, no temporary provision and no sign that the company understands the impact this closure is having on local people.
"This part of Bradford already has some of the lowest car ownership in the country.
"Taking away the only Post Office without warning or replacement is nothing short of negligent.
"Residents deserve better than bland emails and empty assurances."
Cllr Edwards said that he had also approached a local housing association, which owns commercial units in the area, to explore whether an alternative site could be used to restore services - something he claimed the Post Office itself had shown "little urgency" about.
He added: "It should not fall to councillors to chase alternative premises when the Post Office has walked away from its responsibilities.
"Local people across this area of Bradford should not be left without essential services because a national organisation can't be bothered to act."
The T&A put Cllr Edwards' concerns to the Post Office this week.
A Post Office spokesperson said: "We regret that Tong Street Post Office remains closed for operational reasons.
"We recommend that customers use nearby Birkenshaw Post Office, which is open 7am to 8pm Monday to Friday, 8am to 7pm on Saturday and 8am to 5pm on Sunday.
"The branch is accessible by public transport.
"We apologise to customers for the inconvenience."