The court heard that Burton-Cope, who had depression, called paramedics on 29 March 2014 after shaking her son
A woman who killed her baby while she was mentally ill has been given a suspended jail sentence.
Eloise Burton-Cope, 33, admitted the manslaughter of her four-month-old son Leon, who died from head injuries.
At Birmingham Crown Court, Burton-Cope was sentenced to two years in prison, suspended for two years.
Her barrister, Jane Humphryes QC, said she had been "lost in a bureaucratic system short of funding... and passed from department to department".
'No-one to blame'
Sentencing Burton-Cope, who lived at Glebe Road, Deanshanger, Northamptonshire, Mr Justice Haddon-Cave said "no-one should feel guilty about what happened".
The judge said it was "unfortunate" that her medical condition was not recognised at the time but "no-one is to blame", adding "it is very easy to be wise after the event".
The court heard that Burton-Cope, who had depression, called paramedics on 29 March 2014 after shaking her son.
Leon was taken to hospital with a fractured skull and brain damage. He died two days later.
'Total devastation'
Ms Humphryes said: "This was a distressed, tired, mentally ill lady. She was doing her best to look after her child and she panicked.
"There's nothing to suggest she didn't love and care for him.
"Her devastation is total and she will certainly never overcome that.
"She did seek help from medical professionals. She was lost in a bureaucratic system short of funding.
"She was passed from department to department, each one thinking the other was looking after her. There was no proper plan."
Ms Humphryes added: "She will have to live with these tragic events for the rest of her life."
Leon had been "crying for four days" and would not feed properly, the court heard.
Burton-Cope, who now lives in Milton Keynes, suffered bouts of "psychotic behaviour" and had been "hearing voices".
She was last seen by a health visitor on 22 January 2014 and no concerns were raised, the court heard.
Burton-Cope, whose not guilty plea to murder was accepted by the prosecution, admitted manslaughter in June.
