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The pop-up Post Office based at Tonbridge Castle has been closed for over a week and will remain shut until November 17.
The branch has been plagued by staffing issues and poor internet connectivity since it moved there earlier this year.
It could not get a proper connection installed until Thursday of next week.
The Post Office had been housed within WHSmiths in the High Street, but had to move out when the store closed on July 30.
There was a three-month hiatus before temporary accommodation was found at the Castle Gateway.
But from the start, the branch has been unable to offer a full service: no passport checks, driving licence renewals or foreign currency for example.
Recently, its hours of opening have also been reduced by one hour each day and Saturday opening withdrawn.
Mark Hood and Paul Stepto are Green Party councillors representing the Tonbridge division at KCC.
Cllr Hood said: "We have been lobbying the Post Office on this since it first became known they would have to leave WHSmiths back in March.
"We have suggested several alternative locations and provided contact details for the landowners.
"In the meantime, the level of service at the castle has been continually eroding: opening hours have been reduced, but even when customers have found it open, many have been turned away because the Internet connection has failed."
The two councillors asked Kent County Council to open a dialogue with the Post Office with a view to accommodating a branch within Tonbridge Library, as it does at Tenterden and Swanley.
But the company said it had visited the library and found "there was insufficient space" to accommodate its service.
It said it was still searching for retail partners in the town who might take on the branch. Businesses which are interested can visit here.
A Post Office spokesperson said: “We continue to search for a permanent solution. We sincerely apologise for the disruption to the service."
Cllr Hood added: "Their solution has been a disaster from the start. Frankly, it's not good enough."
There are other Post Office branches at York Parade and at Martin Hardie Way in Higham Wood.