In an early paper (Chuang, D. M. and Arapostathis, A., 1999), the ergodic control problem of partially observed Markov chains was studied. A major assumption was proposed to justify the existence of the optimal policy characterized by a dynamic programming equation. In this note we show that the major assumption, though quite general and easily verifiable, is not satisfied by an important class of machine maintenance problems. A modified version of the assumption is thus presented to improve this shortage and an example is analyzed to show our work.