The ability to perform repeated Byzantine agreement lies at the heart of important applications such as blockchain price oracles or replicated state machines. Any such protocol requires the following properties: (1) \textit{Byzantine fault-tolerance}, because not all participants can be assumed to be honest, (2) r\textit{ecurrent transient fault-tolerance}, because even honest participants may be subject to transient ``glitches'', (3) \textit{accuracy}, because the results of quantitative queries (such as price quotes) must lie within the interval of honest participants' inputs, and (4) \textit{self-stabilization}, because it is infeasible to reboot a distributed system following a fault. This paper presents the first protocol for repeated Byzantine agreement that satisfies the properties listed above. Specifically, starting in an arbitrary system configuration, our protocol establishes consistency. It preserves consistency in the face of up to $\lceil n/3 \rceil -1$ Byzantine participants {\em and} constant recurring (``noise'') transient faults, of up to $\lceil n/6 \rceil-1$ additional malicious transient faults, or even more than $\lceil n/6 \rceil-1$ (uniformly distributed) random transient faults, in each repeated Byzantine agreement.