{"statusCode":429,"error":"Too Many Requests","message":"[circuit_breaking_exception] [parent] Data too large, data for

It seems like there is a query triggered by a visualization on that dashboard that becomes very expensive when a full month of data is queried.

A common case is a hardcoded date histogram interval which is set to a small value. Is that the case on your dashboard? What visualizations are you using? Also, what version of Kibana are you running?