The Auger Engineering Radio Array (AERA) is currently the largest facility to measure radio emissions from extensive air showers. Located at the Pierre Auger Observatory in Argentina, it comprises 153 autonomous radio-detector stations, covering an area of 17 km$^2$, and measures radio waves in the frequency range from 30 to 80 MHz. For the correct interpretation of data collected by AERA stations, the detector response has to be carefully calibrated. In the past, this was done by measuring the analogue chain in the laboratory, in addition to simulating and measuring the directional response of the antenna. In this work, we perform an absolute calibration by using the radio emission from the Galaxy. A model of the full radio sky is propagated through the system response, including the antenna, filters and amplifiers, and compared to the average spectra recorded by the stations. The method to determine the calibration constants, as the results, for each antenna will be presented. The behavior of the calibration constants is studied as a function of time from 2014 to 2020. There is no relevant ageing effect over a timescale of 10 years, showing that radio detectors could help to monitor possible ageing effects of other detector systems during long-term operations, stressing their importance in determining an absolute energy scale.