Long Term Evolution Advanced (LTE-A) introduces a new feature called Proximity Services (ProSe) that enables device-to-device (D2D) communication between User Equipment (UE), including the capability to operate out-of-coverage. In order to establish a D2D communication link the UEs need to be synchronized. In out-of-coverage scenarios, the synchronization is performed in a distributed manner by the UEs. In this paper, we studied problems associated with the simultaneous execution of the synchronization procedure by LTE-A D2D-enabled UEs operating out-of-coverage. In particular, we focused on detection and convergence problems resulting from the half-duplex constraint and periodic scheduling. We showed that if two transmitter UEs are acting as synchronization references and they perform the procedure too close in time, convergence to a synchronized state is not possible. Moreover, the periodic triggering of the procedure will make the problematic condition persistent in time. We proposed an effective algorithm that prevent these problems, or resolve them in a reasonable time. We considered the protocol and requirements specified in the LTE-A standard, and we evaluated the performance of the proposed algorithm using system level simulations.