The man, who requested anonymity, said Jessop Maternity Wing was still "refusing access" to partners despite the new guidance issued by the NHS on December 15.
This means, women are now allowed to have one person with them throughout their pregnancy, during labour, birth and their immediate postnatal period as long as their support partner is not showing any coronavirus symptoms.
But he has so far been unable to attend anything with his wife, including an early scan.
He also claimed that his wife had been refused permission to contact him via video calls during any appointment as it was "against hospital policy."
"She had been bleeding and we had spent a week thinking we were losing the baby, I spent this time in the car, while my wife was alone in the hospital.
"Why on earth there is no flexibility on this given the current situation is beyond me.
"Consequently, I still have not heard my child's heartbeat, the most comforting of sounds when you believed you were losing a baby."
On December 17,Sheffield Teaching Hospitals NHS Foundation Trust wrote on its Facebook page that they would provide an update "as soon as any changes are implemented".
The post read: “We are pleased that we now have guidance that will enable partners to attend maternity appointments and scans in the near future, and are currently working through this to ensure that we can implement any changes that are needed in a COVID safe manner.”
An expectant mum, Amy Ryan, also expressed her frustration when she was told the maternity wing had no plans of changing their visitors' guide.
The 32-year-old said: "Hospitals in London are following the guidance, despite their more stricter measures as well as trusts such as Chesterfield who implemented this within days.”
Sheffield Teaching Hospitals, when contacted, said they would have an update tomorrow (December 24) on changes to the guidance.
A spokesperson also clarified that Amy’s partner has been allowed access during labour and that it was a "miscommunication" issue.