Lily has underdeveloped internal organs and an infection, and her parents want to get her home.
But because she does not have travel documents to say she is a New Zealand citizen, she is stuck in China.
She is in a stable condition and strong enough to cope with a medical evacuation flight.
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The Hewgills contacted the New Zealand Embassy in China to find out what arrangements were needed to bring her home and were told it would take up to 2 months to organise the paperwork.
The Ministry of Foreign Affairs and Trade said it was in "regular contact" with the couple.
But Mrs Hewgill said it was not moving quickly enough and she was now facing having to stay in China on her own.
"New Zealand is dragging its feet. We are New Zealanders, we had a baby overseas unexpectedly and we want to bring her home. But it feels like the Government has absolutely abandoned us," she said.
"Greg must return home to return to work. I must stay with the baby. This splits up our family and puts pressure on us emotionally and financially."
Mrs Hewgill spent only one day in hospital after Lily's traumatic birth.
"I had no instructions, I was delivering my first baby, and three months early and I thought someone would be coaching me, at least be helping me. But there was nothing. I had to tell them that the baby was coming and I needed to push. I was in agony, I was begging them for help ... I was screaming. It was appalling."
Mrs Hewgill was born in the US and her husband in Canada, but each has dual citizenship.
Lily was issued a Chinese birth certificate and the US Embassy gave the couple a passport in her name.
"Our lives are in Auckland. Lily is a Kiwi by descent. We are citizens and she is our baby, she should be able to come home. This is ridiculous."
MFAT said it was providing consular support and advice to the parents of the baby.
It had liaised with the Department of Internal Affairs to confirm citizenship and to hurry the issue of emergency travel documents.
