Residents in Staylittle have accused BT Openreach of not responding quickly.
Openreach said engineers are trying to fix the fault which was caused by a thunderstorm.
Other problems with phone lines in the area over recent years include people being able to hear the conversations of neighbours on their own lines.
Resident Alwena Pugh told BBC Radio Wales' Jason Mohammad programme, her husband has an autoimmune disease and is receiving chemotherapy at Morriston hospital in Swansea.
"His consultant is away for a month on holiday and he'd said that all the blood test results would be given over the telephone which is obviously frustrating because our phone sounds like it's ringing - apparently it goes into answering machine," she said.
"I'm sure we've got I don't know how many messages once it comes back on but we're obviously not getting them."
She added: "I'm a carer for an elderly disabled lady. If she happens to have a fall at the night or morning or whenever she needs me she has no contact to get hold of me."
Openreach said the thunderstorm damaged parts of the local network which has affected landlines serving Staylittle.
A spokesman added: "The fault was reported on Monday 24 August and one of our engineers attended on the following day to investigate.
"We would like to thank the local residents for their patience and reassure them that we're working hard to resolve the matter and hope to restore full service to those that have been affected later this week."
About 25 homes in a Powys village which has no mobile signal have not been able to use their landlines for 10 days because of a fault.