Two children died at Kiambu Level 4 Hospital on Thursday morning, allegedly due to lack of oxygen, hours after the President had commissioned it.
President Uhuru Kenyatta also commissioned Sh380 million equipment at the facility on Wednesday.
Henry Ndung'u, one and a half, and three-month-old Stanley Mwangi were admitted with fever the previous morning and put on oxygen support machines.
The children, who were also on medication, died after doctors allegedly refused to respond to a distress call after the machines failed and a blackout followed.
Hospital medical superintendent David Kariuki said the children did not die due to lack of oxygen as the hospital has a steady supply.
He said Henry was diagnosed with Bacterial infection and put on Ceftriaxone, oxygen and maintenance fluid.
"Henry started gasping at 6.33am while on oxygen, resuscitation done but certified dead at 6.45am, i have talked to the parents and explained to them the circumstances surrounding their baby's death", a statement from the superintendent read.
Ndung'u's mother said they had taken him to Nazareth hospital in Ruiru but were referred to Kiambu hospital, where he was admitted at about 6am.
"My child was put on drip and oxygen support. He died after the oxygen machine failed as per what the doctor confirmed," said Esther Wambui.
She said her son had been responding well to medication and was playful, but that a doctor administered a dose obtained elsewhere as the hospital did not have medicine.
Her husband Richard Karanja said: "I was told by the doctor to buy the medicine at a chemist opposite the hospital, at Sh4,500, as the hospital did not have any."
Mwangi's mother Ann Wanjiku declined to speak of the turn of events at the hospital but said she is poor.
Wambui said their children were admitted at about the same time. She said she noticed Mwangi's hands turning blue as their children's beds were in the same area.
The woman said they called for nurses on duty but that there was no response. She said she searched for the nurses but that they they told her off when she talked tot hem.
"When Wanjiku's son started turning grey and blue we called for the nurses in charge but they did not respond. I went to them but they told me we were there to look after our children. Our children died a few minutes later," she said.
A man named John Njagi said his one-year-old son died at the hospital last week after being placed in a machine he did recognise. He said doctors later told him the boy had died but did not give details.
"My son Travis Mbogo died under unclear circumstances. I brought him here because he had a fever but he did not last a day. I was told he died, without any explanation," he said.
In November 2015, an expectant woman named Cecilia Wanjiku died while undergoing an operation after a power outage.