diff --git a/internal/rpc/rpc.go b/internal/rpc/rpc.go
index a96a3ec77..61c443bc7 100644
--- a/internal/rpc/rpc.go
+++ b/internal/rpc/rpc.go
@@ -240,7 +240,7 @@ func RetryStreamingServerStream[Req, Resp any](
 				} else {
 					// Stream terminated; check if this was caused by an error
 					err = stream.Err()
-					logLevel = log.Warn
+					logLevel = logLevelForError(err)
 					break
 				}
 			}
@@ -268,3 +268,12 @@ func RetryStreamingServerStream[Req, Resp any](
 
 	}
 }
+
+// useDebugErrorLevel indicates whether the specified error should be reported as a debug
+// level log.
+func logLevelForError(err error) log.Level {
+	if err != nil && strings.Contains(err.Error(), "connect: connection refused") {
+		return log.Debug
+	}
+	return log.Warn
+}