This paper considers M^[x₁],M^[x₂]/G₁,G₂/1 general Retrial G-queueing system with priority services. Two customers from different classes arrive at the system in two independent compound Poisson processes. Under the pre-emptive priority rule, the server provides a general service to the arriving customers subject to breakdown and Modified server vacation with general (arbitrary) vacation periods. If the system is not empty during a normal service period, the arrival of a negative customer removes the positive customer being in service from the system and causes server breakdown. The repair of the failed server starts after some time known as delay time. After completing the delay time the repair process will start. After completing vacation and repair process the server needs some time to set up the system. The delay time, repair time and set up time follows general distribution. The priority customers who find the server busy are queued and then are served in accordance with FCFS discipline. The arriving low-priority customers on finding the server busy cannot be queued and leave the service area and join the orbit as a retrial customer. They try their luck for service from the orbit. Moreover if the high priority customer is not satisfied with the service given they may join the tail of the queue as a feedback customer with probability p or leave the system with probability q . We consider balking to occur at the low priority customers during server's busy or idle period. The time dependent solutions are derived by using supplementary variable technique and numerical examples are presented.