The communications regulator ComReg has asked An Post for a report on the lack of postal deliveries in parts of south Co Dublin over the past weeks.
Residents from Dún Laoghaire, Ballybrack and Glenageary have made complaints to ComReg and have also rung The Irish Times about not receiving any mail.
They said they were told to go to local sorting offices to collect their mail, where there were long queues.
A spokesman from ComReg said: "We are aware of the situation in Ballybrack and Dún Laoghaire and have raised the matter with An Post and have asked them for a report."
He said ComReg had received a number of calls from the public. The legal position was that An Post was obliged to deliver a service once a day. ComReg is the statutory body responsible for the regulation of the electronic communications and postal sector.
A spokesman for An Post said it was aware of the problems and apologised to customers for the delays. The problem was in the main sorting and delivery office that served the area.
"There have been a number of problems in staffing and a substantial number of staff on sick leave which have led to some cases of a lapse in the delivery service in a number of areas."
Normally there would be a number of staff available to do overtime but that had not happened in this case.
"We apologise to customers. We realise the situation and do appreciate there is a problem. We are addressing it at the moment by sending in a number of extra people."
Last Monday An Post sent in three people who had been trained especially but only one turned up. Next Monday they would be sending in five or six extra people to help existing staff.
"There is a much higher level of sickness that you'd normally expect," he said. The lack of people to do overtime was not due to any dispute.
One caller from Ballybrack said she had not received post for three weeks. Residents were given dockets to collect their mail at a sorting office.
"The situation has slightly improved as we've received some mail but that was posted in February. We haven't had mail for nearly a month. We were told to go to the sorting office.
"It is very serious for some local people as they have been expecting social welfare cheques which haven't come."
A man from Dún Laoghaire said only businesses and expensive estates were receiving mail.
A resident in Glenageary said he had phoned An Post as he knew certain important letters to him had been posted. He was told there was a manpower shortage and that he could collect mail at the delivery office.
There was a queue of angry people there, he said.