The issue is affecting all areas of Old Colwyn and Llysfaen, including the Colwyn and Eirias wards.
Councillor Cheryl Carlisle, of Colwyn ward, said “lots of concerned residents” had reported not having received any letter deliveries for up to 10 days from Royal Mail.
Attempts to contact the sorting office in Colwyn Bay had been to no avail.
“I have been trying to contact the sorting office in Colwyn Bay, and then the wider Post Office network, but that number is no longer in use, and every option you press directs you to a website, not a human,” said Cllr Carlisle.
“Lots of residents are waiting for hospital appointments and urgent mail, so this is a very worrying situation.”
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Royal Mail said local issues such as the one it is claimed is affecting Old Colwyn were usually a result of “temporary resourcing pressures” and that it would “focus on restoring normal service as quickly as possible”.
Cllr Carlisle said the lack of mail being delivered was “not good enough”, and told the Pioneer: “It is all areas of Old Colwyn and Llysfaen too.
“It covers my ward of Colwyn, and the adjoining ward of Eirias, so it is affecting all of Old Colwyn village.
“It seems to be related to the new owners of the Post Office, and not our hard working posture. There just isn’t enough man/woman power apparently.
“Meanwhile, residents are missing hospital appointments and bank cards etc. It’s just not good enough.”
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A Royal Mail spokesperson said: “We know how important it is that customers receive their mail on time, particularly when it includes items such as medical appointments or other important correspondence.
“Recent figures show around 92 per cent of letters arrive on time, but we recognise performance is not yet where it needs to be in all areas.
“Where there are local issues, these are typically caused by temporary resourcing pressures, and we focus on restoring normal service as quickly as possible.”