The continuous positive airway pressure (CPAP) machine is the most effective treatment for the problem because it stops the throat from closing.
But the Ramms are facing an uphill battle to convince doctors to give them the crucial medical kit.
Mrs Ramm, of Dereham, Norfolk, said :
"I don't think it is right that a mother should have to perform CPR on her own baby.
"She goes limp and blue within seconds and I have to pick her up straightaway - and if she doesn't start breathing on her own I have to intervene.
"We have been battling for eight months to get some answers and make progress with Phyllisity's condition so I can't see how it will hurt to have a CPAP trial.
"If that doesn't work at least we will know and we can try something else. "She is not likely to grow out of it so we can't go on like this for ever.
"Phyllisity is such a happy baby, always smiling and making us laugh," said Kylie.
"We love her so much and just want what's best for all of our children.
This is really sad .