The paper investigates the stability of the discrete-time modified unscented Kalman filter (MUKF) in transmitting measurement outputs to the filter via a network. Since the communication channel states do not always vary in time, the arrival of the observations is modeled as a two state time-homogeneous Markov process gamma(k). The stability of the estimation error covariance matrices at packet reception times is analyzed. Sufficient conditions (related to H-k and the initial conditions) for the peak covariance stability and the usual covariance stability are given. Also the relationship between the different types of stability notions is illustrated for systems with i.i.d observation dropouts. Numerical example is given to illustrate the effectiveness of the techniques developed.