Staffing levels on Kyle Ward, where the patient was being looked after, will be investigated as part of the probe.
Health campaigner Rab Wilson, who caused a storm when he blew the whistle on the health board's failure to publish investigations into mistakes last year, worked as a psychiatric nurse in the hospital for more than 20 years.
He said he had raised concerns about staffing levels in the hospital at night during Christmas and New Year a year ago.
Mr Wilson, who no longer works for the health board, said he understood that this New Year an experienced staff member had been moved from Kyle Ward to cover staffing shortages elsewhere.
He claimed of the qualified nurses left working in the hospital, many were bank or agency staff.
He said: "Mental health problems always become worse at Christmas and New Year."
Psychiatric hospitals provide a "community emergency service" and should be staffed appropriately throughout the year, he said.
Mr Wilson added: "There needs to be a serious look at the way NHS Ayrshire and Arran wards are staffed over Christmas and New Year."
He explained some patients admitted to the hospital would need to be under constant observation, which meant someone sitting in a chair at the door of their room.
This, he said, could have a significant impact on staffing resources.
Jim Crichton, director of primary care and mental health services for NHS Ayrshire and Arran, said: "Our deepest sympathies are with the family concerned. When a tragic event such as this occurs it is treated as a significant adverse event and our rigorous review procedure is activated.
"This includes support for staff and families to enable them to be involved in the review and mechanisms to ensure learning is shared."
Mr Wilson spent more than five years trying to obtain copies of serious incident reports from NHS Ayrshire and Arran hospitals. He took his battle to the Scottish Information Commissioner who heavily criticised the board for failing to release the documents last year.
Health Secretary Nicola Sturgeon went on to order an inquiry into the situation.
New guidelines on dealing with serious incidents within the NHS are being rolled out across Scotland following the scandal and NHS Ayrshire and Arran has implemented an improvement plan.