This will be fixed in the next release of ArcGIS Explorer desktop. It is just taking longer to get an update out than we had originally planned.
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I experienced the same difficulty. I don't think ArcGIS Explorer can use services when adding the service using the web adaptor. I added my server (which is not publically accessible) to ArcGIS Explorer twice, it the exact same server but one is using the web adaptor and the other is bypassing it.
Now they are both added and can connect and I can even see my layers on the list but when I add it to the map from my web adaptor URL then it adds but doesn't show up.
However when bypassing the web adaptor and using 6080 with the fully qualified domain name with "/ArcGIS/Services" at the end, my layers show up on map. Hopefully this will help.