An air-fuel-ratio control device is known which includes an exhaust gas sensor (so-called linear air-fuel ratio sensor or oxygen sensor) in an exhaust passage of an internal combustion engine in order to control an air-fuel ratio of the internal combustion engine by way of feedback control.  Moreover, a structure is known in which an exhaust gas sensor is provided downstream from a catalytic device in addition to an exhaust gas sensor provided upstream from the catalytic device in order to further improve an accuracy of the air-fuel ratio control. 
A responsivity of output of such an exhaust gas sensor might be worsened due to secular degradation or thermal degradation.  Hence, various degradation diagnosis devices have been previously proposed.  Patent Literature 1 discloses to perform a degradation diagnosis on the basis of a reversal period of an output signal of the exhaust gas sensor.  Specifically, since this reversal period is influenced by a load of the internal combustion engine, i.e. by an intake-air quantity, a degradation-determination threshold value is set at a smaller value as an accumulated intake-air quantity over a predetermined diagnosis period becomes larger.  Then, it is determined that the exhaust gas sensor is in a degraded state, when the detected reversal period is longer than the degradation-determination threshold value. 
The degradation diagnosis device disclosed by Patent Literature 1 is constructed based on a recognition that a certain quantity of exhaust gas (accumulation value) needs to flow through the exhaust gas sensor in order to attain the reversal of the output of the exhaust gas sensor.  In a case that the intake-air quantity (a flow quantity per unit time) is relatively large, the certain quantity of exhaust gas (accumulation value) is realized in a relatively short time.  Hence, in this case, the degradation-determination threshold value for the reversal period is set at a relatively small value.  The technique of Patent Literature 1 is intended for the exhaust gas sensor located upstream from the catalytic device. 
However, in a degradation diagnosis for the exhaust gas sensor located downstream from the catalytic device, a variation of exhaust composition around the exhaust gas sensor is influenced by an oxygen storage capacity of the catalytic device.  Moreover, an exhaust-gas quantity (accumulation value) required to attain the output reversal of the exhaust gas sensor is affected by a flow velocity of exhaust gas flowing through the catalytic device.  That is, according to a new finding of the inventors of the present application, in the case of the downstream-side exhaust gas sensor, a great deal of exhaust gas (accumulation value) is necessary to attain the reversal of the output of the exhaust gas sensor if the flow velocity of exhaust gas passing through the catalytic device and the downstream-side exhaust gas sensor is high.  In other words, when the intake-air quantity (flow quantity per unit time) is large, the flow velocity of exhaust gas passing through the catalytic device and the downstream-side exhaust gas sensor is high, so that the exhaust gas quantity (accumulation value) or the intake-air quantity (accumulation value) necessary for one-time reversal of the output is large. 
In the degradation diagnosis device disclosed by Patent Literature 1, such an influence from the flow velocity has not been considered.  Hence, a proper diagnosis for the downstream-side exhaust gas sensor cannot be carried out.