WMS by design is for viewing the maps over the web, there is no way to download the data through WMS. To download you have quite a few options from ArcGIS Server WFS, WCS, KML or ArcGIS Server Feature Service etc.
Although the question is old, but the problem is still valid. So I thought it might be worth to mention another solution: WMS Downloader. It is available as the ArcGIS Addin as well as a standalone Windows app. Disclaimer: I'm one of the coauthors of this add-in and this is a licensed product. Feel free to check the trial version.
