This paper considers a perishable inventory system with a single unreliable server where the customers arrive in an exponentially distributed time interval and demand a single item. The inventory is purchased from an outside source and the control policy is (s, Q). On arrival, a customer leads to service if the server is available and the inventory is non-empty. The server may break down while at service and it follows Poisson distribution. The arriving customer on finding the server busy or breakdown goes to a waiting place of infinite capacity called orbit, with pre-allotted probability or exits the system with complementary probability. Each customer in the orbit retries to enter the service facility following a Poisson distribution. After every unsuccessful retrial, the customer returns to the orbit with a pre-determined probability or is lost forever with a probability equal to its complement. An algorithmic solution to the problem is obtained using the Matrix Analytic Method. The mean number of customers lost before and after entering the system, the rate of successful retrials among overall retrials and some other performance measures of the system are derived. The impacts of system parameters on different measures are numerically studied. A suitable profit function is constructed and the optimum control policy is numerically obtained.