Lily Duffy, who was born prematurely at 27 weeks, needs her tracheostomy tube cleared of saliva to ensure she does not choke to death.
Previously the role was carried out on a voluntary basis by pupil support assistants at the Glasgow council-run nursery but they now say it is not in their job description.
Her aunt, Alison Kelly, 55, says Lily is missing out learning Makaton, a form of sign language, physiotherapy to help her learn to walk and meeting other children.
Ms Kelly, from Croftfoot, Glasgow, who has written to Scotland's First Minister Alex Salmond, said: "When Lily was first assessed, the pupil support workers were doing it on a voluntary basis.
"The unions are saying they want more money and they are right. The nurses say it is not their role.
"She now has just three hours of nursery education rather than three days.
"She's due to start school so we are concerned. She's a sociable wee girl and missing out on the interaction with her peers.
"I feel they are discriminating against her human right to breathe."
Kelbourne Park Nursery has a nurse and a health care assistant but they have also refused to carry out the procedure.
Glasgow City Council and officials from Unison are locked in a dispute about the medical care of pupils with additional needs and support assistants are taking part in industrial action.
Carol Bell, Unison's education convener, said: "Tracheotomy care is technical work, medically, and some of our members have felt uncomfortable doing this.
"It could be a life or death situation. There is a fully qualified nurse in school and a health care assistant."
An NHS Greater Glasgow and Clyde spokeswoman said: "Our nursing staff trained and supervised educational staff to provide the care required."
A council spokeswoman said: "We have identified a voluntary organisation that will carry out a full assessment as soon as possible so that Lily can return to the nursery for her full entitlement."