This paper is concerned with the boundedness of the solution of a random Riccati difference equation arising from Kalman filtering with observation losses characterized by a Markovian binary jump parameter. A new sufficient condition for stability in the peak covariance sense is obtained which has a simpler form and is shown to be less conservative for systems with the observability index of two than existing works. Meanwhile, we give some conditions under which the covariance matrix is bounded or unbounded in the usual sense. Then the equivalence between the peak covariance stability and the usual covariance stability is established for systems with the observability index of one and independent and identically distributed (i.i.d.) observation losses.