The incident happened at about 18:45 on Saturday about 100m from the harbour at St Abbs.
The woman was pulled from the water unconscious and given oxygen and then taken to Aberdeen Royal Infirmary.
The RNLI announced last month it intends to shut the station with cover being provided from nearby Eyemouth.
The rescue came just 24 hours after about 80 people attended a meeting to oppose the closure plans.
A petition with 3,000 signatures has also been gathered.
The RNLI announced last month that the St Abbs boat was no longer needed and in future cover would be provided with an additional boat in nearby Eyemouth.
It has rejected claims that lives would be put at risk by the move and said it was about having the "right assets in the right place".
A lifeboat crew at a closure-threatened station has been called out to rescue a diver in distress from the waters off the Borders coast.