According to the Open GIS Consortium Web Map Service (WMS) version 1.1.1 specifications, "layers may include a <ScaleHint> element that suggests minimum and maximum scale for which it is appropriate to display this layer." Minimum and maximum scales will be reported in the WMS service capabilities -
<a href='http://support.esri.com/en/knowledgebase/techarticles/detail/27948' target='_blank'>How To: View the WMS service capabilities</a> - and in the Layer Properties General Tab for the WMS service layer and all service sublayers.
It is possible that the WMS layer's visibility in ArcMap will not adhere exactly to the specified minimum and maximum scale range values reported in the General Tab.
WMS output is designed to accommodate output devices of arbitrary size and resolution. Defining scale as the ratio of map size to real-world size is not appropriate. Since there may be resolution differences between the server and the ArcMap client, layers may not draw precisely at their reported scales.