The health board said it had to take the "significant step" last Thursday after sustained and continuing demands at ARI.
Patients were diverted to Dundee and Elgin where "clinically appropriate", although life-saving care was still delivered at ARI.
After it was stood down, health chiefs said the hospital had entered a "recovery phase" and there would be a review of the incident.
The August letter to senior management said: "Over the past 12 months multiple risks have been reported and recorded from all areas of the portfolio, both formally and informally.
"Despite this, we are experiencing a deterioration in the performance against most measures and targets and the quality of care we are able to deliver to patients.
"We are increasingly concerned about the impact this sustained pressure and risk is having on our staff. We see regular evidence of individuals and teams who are experiencing harm from the required workload and inability to deliver effective care for patients with the resources available."
It added: "We are aware that these concerns have been escalated previously and despite reassurances, this has not resulted in any significant improvement."
The critical issues raised included staff wellbeing and longer term improvement.
"The current trajectory of performance and occupancy across MUSC in recent months suggests continuous deterioration," the letter said.
"There is no evidence to support any planned improvement work or capacity changes that will meet the impending increase in demand seen over October and sustained over [the] winter period.
The letter said the authors were aware of the financial pressure across NHS Grampian and the extent of the projected overspend.
