A frequency stabilized laser capable of long-term autonomous operation is the basis for the continuous operation of an atomic fountain clock. In this paper, based on a 780 nm commercial external cavity diode laser used in the ⁸⁷Rb fountain clock, we develop a long-term automatic frequency stabilization system by using an embedded system. The proposed system can automatically identify the target peak in the ⁸⁷Rb saturated absorption spectrum, stabilize the laser frequency for a long time and quickly re-lock it after an accidental loss of lock. In addition, we develop a method for dynamically adjusting the operating point. The target operating point changes with time because the influences of temperature, humidity, device aging, and other factors during the long-term operation of the laser. Based on this method, the laser frequency stabilization system makes lock loss rarely occur, and easily re-locks even if lock loss happens. The proposed frequency stabilization system has been successfully applied to our transportable ⁸⁷Rb fountain clock. The clock can operate normally soon after transport and the long-term stabilization time of laser frequency can reach more than one month. The long-term stability of laser frequency relative to the ⁸⁷Rb saturated absorption spectrum is about 2.3×10 ^-13 and the long-term stability of the transportable ⁸⁷Rb fountain clock before and after transport is always at the magnitude of 10 ^-16.