Abstract In order to predict the quality and the stability properties of milling processes, the relevant dynamics reduced to the cutting edges needs to be known. However, the dynamics varies through the workspace along the tool path during a given machining operation. This is the case for large heavy duty milling operations, where the main source of the relevant dynamics is related to the otherwise slowly varying machine structure rather than to the fairly steady milling tool dynamics. The effect of slowly varying dynamic parameters is presented for milling stability when the cutting process takes place in a region of the work space where the steady-state cutting would change from stable to unstable. After the separation of the slow and fast time scales, the governing non-autonomous delay differential equation is frozen in slow-time in order to determine the time-periodic stationary cutting solution of the milling operation for different parameters. The loss of stability is predicted from the correction to the time-periodic frozen time solution, for which we obtained non-autonomous equation for the accumulated growth over the slow-time. The growth shows loss of stability with a shift on the parameters compared to the static parameter solution.