We synthesized a self-oscillating polymer chain with a negatively charged moiety. The polymer chain caused the aggregation-disaggregation self-oscillation under the constant temperature induced by the Belousov-Zhabotinsky (BZ) reaction. In this study, we investigated the influence of temperature and the concentration of sodium bromate on the aggregation-disaggregation self-oscillation of the polymer solution (1.0 wt%) in a strongly acidic condition. As a consequence, we clarified that the life-time of the self-oscillation increased with decrease in the concentration of sodium bromate. On the other hand, the lifetime of the self-oscillation decreased with increase in temperature. In high temperature condition (48 and 60 °C), the amplitude of the self-oscillation was significantly inhomogeneous. Moreover, the frequency of the self-oscillation increased with increasing temperature. On the other hand, the frequency decreased with increase in the concentration of sodium bromate. This tendency was opposite to that in the acid-free condition and the 2.0 wt% AMPS-containing polymer solution.