It comes after the health board reported that the hospital in Melrose was at capacity earlier this month.
On Tuesday, April 12, chief executive of NHS Borders Ralph Roberts, said that the hospital was under “extreme pressure” and all beds were full.
As a result, the accident and emergency department was exceptionally busy, with a number of people requiring admission, and the public were asked to ring 111 before going to A&E.
Mr Roberts said that staff were working round the clock to care for patients and added that it was “a very challenging situation”.
He also appealed to Borderers to be patient with the local health teams as they attempted to manage a packed hospital with depleted staff numbers.
Recent figures showed just 61 per cent of people who attended the accident and emergency department at the BGH were seen within four hours.
Mrs Hamilton has previously written about various issues pertaining to the performance of the BGH.
However, she now believes that the situation has deteriorated to a level where urgent intervention is required.
She said: “Constituents, quite rightly, contact me on a regular basis expressing their concern about their treatment and that of their family members or friends in the Borders.
“It has got to a point where it simply cannot continue like this, and I have written to the Health Secretary calling for urgent action to address the issues raised in my letter.
“Hardworking staff are doing a fantastic job, yet the lack of resources from the SNP Government means they are put under pressure.
“It is simply unacceptable that targets are being missed and the hospital was a full capacity.
“I want to see the SNP Government properly resource the BGH to prevent these issues arising again as we head into the summer months.”